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# Combined Probability question

Author Message
Intern
Joined: 17 Nov 2009
Posts: 35
Schools: University of Toronto, Mcgill, Queens

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Updated on: 06 Apr 2010, 03:21
21
70
Hi All,

There are lots of probability questions which I found in this forum which worth practicing once you have them in one place. I copied them from this forum and all the credit goes to the original posters.

Useful website to learn the simple probability.
http://gwydir.demon.co.uk/jo/probability/info.htm

1. Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?
A: 1/5
B: 1/4
C: 3/8
D: 2/5
E: 1/2

#p654985

2. Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.
Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?

A 8/33
B 62/165
C 17/33
D103/165
E 25/33

56530.html

3. A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?

1)
2)
3)
4)
5)

snappy-dresser-p-86872.html

4. In the xy- plane, a triangle has vertexes (0,0), (4,0) and (4,5). If a point (x,y) is selected at random from the triangular region, What is the probability that x-y>0 ?

A. 1/5
B. 1/3
c. 1/2
D. 2/3
E. 4/5

[url]what-is-the-probabilty-such-that-x-y0-86926.html[/url]

5. Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?

(A) 1/4
(B) 1/5
(C) 5/26
(D) 12/42
(E) 13/42

http://gmatclub.com/forum/probability-playing-cards-86902.html

6. Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?

(A) 1/4
(B) 1/5
(C) 5/26
(D) 12/42
(E) 13/42
http://gmatclub.com/forum/probability-playing-cards-86902.html

7 . At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?

# \frac{1}{12}
# \frac{5}{14}
# \frac{4}{9}
# \frac{1}{2}
# \frac{2}{3}

http://gmatclub.com/forum/prob-gclub-diagonostics-86830.html

8 . A committee of three people is chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
1. 16
2. 24
3. 26
4. 30
5. 32

http://gmatclub.com/forum/gmatprep-ps1-86809.html

9 . A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

A) 1/ 2^4

B) 1/2^3

C)1/2^5

D) None of the above

http://gmatclub.com/forum/probability-coin-toss-57447.html

10 . A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is less than 0.2 that the first sock is black.

(2) The probability is more than 0.8 that the first sock is white.

http://gmatclub.com/forum/probability-socks-86757.html

11. Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?

A) 1/24
B) 1/8
C) 1/4
D) 1/3
E) 3/8

http://gmatclub.com/forum/4-letters-4-envelopes-85167.html

12. A team has record of 12 wins and 13 losses for the season. Three games remain and if the probability of winning each remaining game is ½ and there are no draws. What is the probability that team finish the season with the winning record?
1. 1/8
2. ¼
3. 3/8
4. ½
5. 5/8

http://gmatclub.com/forum/probability-of-team-s-winning-86130.html

13. Suppose you play a game where you role a single dice and whatever you roll you get that dollar amount. For example, if you roll a 1 you get $1. If you roll a 6 you get$6. If you are unhappy with the first roll, you can roll again. However, if you get lower the second time, you cannot take the first roll. If you are unhappy with the second roll you can roll a third and final time. Again, if you get lower on the third roll, you have to keep this roll and cannot take the first or second roll.

What is the expected value of this game?

http://gmatclub.com/forum/tough-probability-question-86298.html

14 . If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

http://gmatclub.com/forum/coins-58357.html

15 . In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

http://gmatclub.com/forum/why-the-worst-case-scenario-86217.html

16. Say you have 5 coins. 1 coin has heads on both sides and the other 4 coins are normal (heads on one side, tails on the other)

A coin is selected at random and flipped five times, each time landing on heads. What is the probability that this coin is the coin that has heads on each side?

Edit: the URL doesn't work, so I removed it

17. In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?

5/21
3/7
4/7
5/7
16/21

http://gmatclub.com/forum/4000-possible-combination-84435.html

18. Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one
correct combination.

1 1
2 159/160
3 157/160
4 3/160
5 0

http://gmatclub.com/forum/4000-possible-combination-84435.html

19. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?

A.1/10
B.4/9
C.1/2
D.3/5
E.2/3

http://gmatclub.com/forum/probability-problem-82708.html

20. A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

http://gmatclub.com/forum/4-red-chips-and-2-blue-chips-85987.html

21. A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

1/190

1/20

1/19

1/10

1/9

http://gmatclub.com/forum/probability-that-they-are-matching-shoes-85916.html

22. There are 5 white balls and 3 red balls in a Jar. What is the probability-

1) if someone picks 2 balls without replacing, that 1 ball is white and the other is red?
2) what is the probability that the first ball is red and the second is white without replacing?

3) if someone picks 2 balls with replacing, that 1 ball is white and the other is red?
4) what is the probability that the first ball is red and the second is white with replacing?

http://gmatclub.com/forum/red-ball-white-ball-85748.html

23. Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag WITH replacement. What is the probability that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?

http://gmatclub.com/forum/probability-colored-balls-55253.html

24. In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?
a. (13^4) x 48 x 47
b. (13^4) x 27 x 47
c. 48C6
d. 13^4
e. 13^4(6^3 + 88)

http://gmatclub.com/forum/ps-probability-85690.html

25. There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?
a) 1/n!
b) n/n!
c) 1/n^y
d) 1/n^(y-1)
e) n/y^n

http://gmatclub.com/forum/ps-probability-there-are-y-different-travelers-84216.html

26. A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?

1/4
3/10
2/5
5/12
½

http://gmatclub.com/forum/gmat-club-probabily-question-not-really-probability-84334.html

27. The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two visitors will buy a pack of candy?

* 0.343
* 0.147
* 0.189
* 0.063
* 0.027

http://gmatclub.com/forum/probability-85523.html

29. ill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.

Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?

a. 8/33
b. 62/165
c. 17/33
d. 103/165
e. 25/33

http://gmatclub.com/forum/pc-84892.html

30. A certain telephone number has seven digits. If the telephone number has the digit zero exactly 3 times, and the number 1 is not used at all, what is the probability that the phone number contains one or more prime digits.

a] 1/24
b] 1/16
c] 1/2
d] 15/16
e] 23/24

http://gmatclub.com/forum/telephone-number-with-seven-digits-85304.html

31. The oasis output of Abu Ilan in the heart of the Negev desert, has a population of 20 Bedouin tribesmen and 20 Farma tribesmen. El Kamin, a nearby oasis, has a population of 32 Bedouin tribesmen and 8 Farima tribesmen. A lost soldier (from another country), accidentally seperated from his army unit, is wandering through the desert and arrives at the edge of one of the oases. The soldier has no idea which oasis he has found, but the first person he spots from a distance is a Bedouin. What is the probability that he wandered into Abu Illan? What is the probability that he is in El Kamin?

http://gmatclub.com/forum/probability-85473.html

32. There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

http://gmatclub.com/forum/permutation-combinations-84337.html

33. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?

A. 3
B. 7
C. 8
D. 9
E. 11

http://gmatclub.com/forum/probability-question-85216.html

34. Magician has a rabbit in the hat, it's either white or black (probability 50/50). He adds one more rabbit in the hat which is white and then he randomly picks one which turns out to be white. What is the probability that the remaining rabbit in the hat is also white?

A. 0
B. 1/3
C. 1/2
D. 2/3
E. 1.

http://gmatclub.com/forum/magician-with-the-rabits-85118.html

35. A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9

http://gmatclub.com/forum/tough-and-tricky-6-probability-of-drawing-85183.html

36. How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?

A. 1
B. 2
C. 3
D. 4
E. 5

http://gmatclub.com/forum/tough-and-tricky-3-leap-year-85179.html

37. If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?

A. 25%
B 50%
C 62.5%
D. 72.5%
E. 75%
http://gmatclub.com/forum/tough-and-tricky-probability-of-integr-being-divisible-by-85186.html

38. Suppose you're given the choice of three boxes. In one of them is the big prize (full-ride from Stanford/Harvard/Any you like); in the others, an apples. The prize and the apples were placed randomly in the boxes. The rules of the game are as follows: After you have chosen a box, the box remains closed for the time being. Then one of the two remaining boxes is opened, (by the computer which knows what is in each box) and the box contains an apple (as far as there are two boxes with apples it's always possible to open one no matter what is in the box you chose). After one box with apple is opened, you are asked to decide whether you want to stay with your first choice or to switch to the last remaining box.

A. What is the probability of winning the prize if you stay with your first choice?

B. What is the probability of winning the prize if you switch to the last remaining box?

http://gmatclub.com/forum/very-interesting-problem-85030.html

39. Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter she prepared an envelope with its correct address. If the 4 letters are to be put in 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?

And seems that it was confusing for many. GMAT often has similar questions, so find below the problems to master yourself in them.

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter she prepared an envelope with its correct address. If the 4 letters are to be put in 4 envelopes at random, what is the probability:

A. That no letter will be put into the envelope with its correct address?

B. That all letters will be put into the envelope with its correct address?

C. That only 1 letter will be put into the envelope with its correct address?

D. That only 2 letters will be put into the envelope with its correct address?

E. That only 3 letters will be put into the envelope with its correct address?

F. That more than one letter will be put into the envelope with its correct address?

G. That more than two letters will be put into the envelope with its correct address?

http://gmatclub.com/forum/letter-arrangements-understanding-probability-and-combinats-84912.html

40. In the poker game Five-Card Draw, each player is dealt a hand consisting of 5 cards from a deck of 52 cards. Each card in the deck has a suit (clubs, hearts, diamonds, or spades) and a value (A, 2,..., 10,J,Q,K).

A. What is the probability that we are dealt a four-of-a-kind?

B. What is the probability that we are dealt full house? (A full house is a hand with both a three-of-a-kind and a two-of-a-kind.)

C. What is the probability that we are dealt two pairs? (Fifth is different)

D. What is the probability that we are dealt three of a kind? (Others are different)

E. What is the probability that we are dealt one pair? (Others are different)

F. What is the probability that we are dealt all five of different ranks?

G. What is the probability that we are dealt hands with every suit?

http://gmatclub.com/forum/let-s-play-poker-84956.html

41. In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

a) 23.
b) 20.
c) 24.
d) 17.
e) 25.

http://gmatclub.com/forum/can-anyone-solve-this-probability-question-84965.html

42. There are 6 cards bearing numbers 2, 4, 5, 5, 5, 6. If two cards are randomly selected from the lot, what is the probability that the difference between the numbers on these cards is 3 or less?

http://gmatclub.com/forum/probability-difference-54650.html

43. A certain basket contains 10 apples, 3 of which are green and 7 of them are red. If three different apples are selected at random from the basket, what is the probability that 2 of them are red and 1 of them is green.
1. 7/40
2. 7/20
3. 49/100
4. 21/40
5. 7/10

http://gmatclub.com/forum/combprob-from-gmatprep-84825.html

44. if two of the four expressions x+y, x+5y, x-y and 5x-y are chosen at random, what is the probability that their product will be of the form $$x^2 - (by)^2$$

1. ½
2. 1/3
3. ¼
4. 1/5
5. 1/6

http://gmatclub.com/forum/combprob-from-gmatprep-84772.html

45. A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?

a) 37/256

b) 56/256

c) 65/256

d) 70/256

e) 81/256

http://gmatclub.com/forum/ps-another-probability-56814.html

46. A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?

1/4
1/2
1/2
5/8
2/3
3/4

http://gmatclub.com/forum/3-yellow-balls-and-5-black-balls-84530.html

47. Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary.

What is the probability that only girls will be elected?

What is the probability that only boys will be elected?

What is the probability that at least one girl will be elected?

http://gmatclub.com/forum/comb-none-56860.html

48. For one toss of a certain coin,the probability that the outcome is heads is 0.6.If this coin is tossed 5 times,which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4*(0.4)
D. 4(0.6)^4*(0.4)+(0.6)^5
E. 5(0.6)^4*(0.4)+(0.6)^5

http://gmatclub.com/forum/probability-84565.html

49. A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

1/14
1/7
2/7
3/7
1/2

http://gmatclub.com/forum/probability-56037.html

50. The choir consists of 5 boys and 6 girls. In how many ways can the singers be arranged in a row, so that all the boys are together? (assume all members of the group are uniform and combinations within the group do not matter).

A 120
B 30
C 24
D 11
E 7

http://gmatclub.com/forum/ps-probability-chord-53774.html

51. In a fantasy football game ended 3:2, what is the probability that the side that lost scored first?

1/4
3/10
4/10
5/12
1/2

http://gmatclub.com/forum/challenge-ratios-and-probability-54794.html

52. If an integer n is to be chosen at randon from the integers 1 to 96 inclusive, what is the probability that n(n+1)(n+2) will be divisible by 8?

a) 1/4
b) 3/8
c) 1/2
d) 5/8
e) 3/4.

http://gmatclub.com/forum/probability-55421.html

53. If the probability that Mike can win a championship is 1/4, and that of Rob winning is 1/3 and that of Ben winning is 1/6, what is the probability that Mike or Rob win the championship but not Ben?

http://gmatclub.com/forum/probability-of-winning-58670.html

54. Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person sub committees, what percent of all the possible subcommittees that include Michael also include Anthony?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

http://gmatclub.com/forum/power-prep-subcommittee-58887.html

55. if x^2 + y^2 = r^2 is the equation of the circle with centre as origin and radius as r.

Point (P,Q) is randomly selected inside the above circle. What is the probability that P>Q>0 ?

http://gmatclub.com/forum/probability-of-a-spot-in-a-circle-84254.html

56. Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny$1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than$10 but less than \$15?

A) 5/16
B) 1/2
C) 12/30
D) 15/32
E) 3/8

http://gmatclub.com/forum/probability-problem-kate-and-danny-each-have-84215.html

Challenge Question

57. A lottery game works as follows: The player draws a numbered ball at random from an urn containing five balls numbered 1, 2, 3, 4, and 5. If the number on the ball is even, the player loses the game and receives no points; if the number on the ball is odd, the player receives the number of points indicated on the ball. Afterward, he or she replaces the ball in the urn and draws again. On each subsequent turn, the player loses the game if the total of the numbers becomes even, and gets another turn (after receiving the number of points indicated on the ball and then replacing the ball in the urn) each time the total remains odd.

(a) What is the probability that the player loses the game on the third turn?

http://gmatclub.com/forum/high-caliber-probability-83206.html

-Bullet

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Originally posted by Bullet on 25 Nov 2009, 12:42.
Last edited by dzyubam on 06 Apr 2010, 03:21, edited 1 time in total.
deleted the broken URL
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25 Nov 2009, 13:41
1
Great job!
+1
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08 Dec 2014, 05:37
Hi Guys

Any idea where I can find the explanations for the first few questions? The link placed above doesn't seem to have them. Cheers
Math Expert
Joined: 02 Sep 2009
Posts: 48110

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08 Dec 2014, 05:43
rvc27 wrote:
Hi Guys

Any idea where I can find the explanations for the first few questions? The link placed above doesn't seem to have them. Cheers

All those questions are discussed on the forum. So, you can use SEARCH to find:
two-couples-and-one-single-person-are-seated-at-random-in-a-92400.html
a-man-chooses-an-outfit-from-3-different-shirts-2-different-91717.html
in-the-xy-plane-a-triangle-has-vertexes-0-0-4-0-and-86926.html

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html

Hope it helps.
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23 Jan 2018, 22:37
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Re: Combined Probability question &nbs [#permalink] 23 Jan 2018, 22:37
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# Combined Probability question

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