Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 May 2015, 13:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Two dice are tossed once. The probability of getting an even

Author Message
TAGS:
Intern
Joined: 15 Mar 2010
Posts: 16
Followers: 0

Kudos [?]: 13 [1] , given: 0

Two dice are tossed once. The probability of getting an even [#permalink]  23 Jan 2012, 20:20
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:17) correct 57% (01:16) wrong based on 275 sessions
Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

A. 1/36
B. 3/36
C. 11/36
D. 20/36
E. 23/36
[Reveal] Spoiler: OA
Intern
Joined: 26 Dec 2011
Posts: 6
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Probability - tossing two dice [#permalink]  23 Jan 2012, 20:58
total possible outcomes for two dice: 36

case 1
prob of getting an even number on the first die
first die can have 2,4,6 second die can have any of 1,2,3,4,5,6
or favorable outcomes 3x6 = 18
probability= 18/36

case 2
getting a sum of 8 (2,6)(6,2)(3,5)(5,3)(4,4)
probability=5/36

now both of the above cases have some cases common to them
i.e. when the first die has an even number and the sum is also 8
there are 3 cases of this kind (2,6) (6,2) (4,4)
prob=3/36

also P(A or B)=P(A) + P(B) - P(A & B)
so we have P(even or sum of 8) = 18/36 + 5/36 - 3/36
20/36
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4227

Kudos [?]: 41005 [1] , given: 5654

Re: Probability - tossing two dice [#permalink]  24 Jan 2012, 01:47
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
Macsen wrote:
Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is
A. 1/36
B. 3/36
C. 11/36
D. 20/36
E. 23/36

OR probability:
If Events A and B are independent, the probability that Event A OR Event B occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur: $$P(A \ or \ B) = P(A) + P(B) - P(A \ and \ B)$$.

This is basically the same as 2 overlapping sets formula:
{total # of items in groups A or B} = {# of items in group A} + {# of items in group B} - {# of items in A and B}.

Note that if event are mutually exclusive then $$P(A \ and \ B)=0$$ and the formula simplifies to: $$P(A \ or \ B) = P(A) + P(B)$$.

Also note that when we say "A or B occurs" we include three possibilities:
A occurs and B does not occur;
B occurs and A does not occur;
Both A and B occur.

AND probability:
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events: $$P(A \ and \ B) = P(A)*P(B)$$.

This is basically the same as Principle of Multiplication: if one event can occur in $$m$$ ways and a second can occur independently of the first in $$n$$ ways, then the two events can occur in $$mn$$ ways.

BACK TO THE ORIGINAL QUESTION:
Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is
A. 1/36
B. 3/36
C. 11/36
D. 20/36
E. 23/36

1. The probability of getting an even number at the first die is 1/2 (as the probability of even = the probability of odd = 1/2);
2. The probability of getting a total of 8 is 5/6^2, as there are 5 different favorable scenarios: (2,6), (6,2), (3,5), (5,3) and (4,4);
3. The probability of getting an even number at the first die AND a total of 8 is 3/6^2 (from above case);

Hence, The probability of getting an even number at the first die OR a total of 8 is 1/2+5/36-3/36=20/36.

_________________
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1725
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 74

Kudos [?]: 437 [0], given: 109

Re: Two dice are tossed once. The probability of getting an even [#permalink]  19 Feb 2012, 07:18
+1 D

Great question.
Remember that the "OR formula" is:

P(A) OR P(B) = P(A) + P(B) - P(A and B)

In this case, A and B can take place together, so the value of P(A and B) is greater than 0.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Director
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 34 [0], given: 7

Re: Two dice are tossed once. The probability of getting an even [#permalink]  21 Feb 2012, 01:10
Bunuel, could you please explain why the probability of getting 'four' on both dices is 1/36 and not 1/18? Why don't we make a difference between 4 on dice 1 and four on dice ?

I mean why the combination 4'4'' is the same as 4''4' (apostrophe symbolizes the dice: ' = dice number one, '' = dice number two).

I have encountered many probability problems, where events that are identical are differentiated. For example:

Quote:
A 5 meter long wire is cut into two pieces. 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 is cut at an arbitrary point?

1/6
1/5
3/10
1/3
2/5

OA:
[Reveal] Spoiler:
(E)

In the example above the probability is 2/5.

Could you please explain the difference?

Last edited by nonameee on 21 Feb 2012, 01:24, edited 1 time in total.
Director
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 34 [0], given: 7

Re: Two dice are tossed once. The probability of getting an even [#permalink]  21 Feb 2012, 01:18
One more question: When calculating probability, how should we know when to count the same instances and when not?
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4227

Kudos [?]: 41005 [0], given: 5654

Re: Two dice are tossed once. The probability of getting an even [#permalink]  21 Feb 2012, 01:38
Expert's post
nonameee wrote:
Bunuel, could you please explain why the probability of getting 'four' on both dices is 1/36 and not 1/18? Why don't we make a difference between 4 on dice 1 and four on dice ?

I mean why the combination 4'4'' is the same as 4''4' (apostrophe symbolizes the dice: ' = dice number one, '' = dice number two).

We can get combination of (2, 6) in two ways: 2 on die A and 6 on die B OR 2 on die B and 6 on die A;

Whereas (4, 4) has only one combination: 4 on on die A and 4 on die B, it has no second combination, since 4 on die B and 4 on die A is exact same combination.

nonameee wrote:
I have encountered many probability problems, where events that are identical are differentiated. For example:

Quote:
A 5 meter long wire is cut into two pieces. 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 is cut at an arbitrary point?

1/6
1/5
3/10
1/3
2/5

OA:
[Reveal] Spoiler:
(E)

In the example above the probability is 2/5.

Could you please explain the difference?

This is completely different problem. In order the area of a square to be more than 1 the side of it must be more than 1, or the perimeter more than 4. So the longer piece must be more than 4. Look at the diagram.

-----

If the wire will be cut anywhere at the red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Also discussed here: a-5-meter-long-wire-is-cut-into-two-pieces-if-the-longer-106448.html

Hope it helps.
_________________
Director
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 34 [0], given: 7

Re: Two dice are tossed once. The probability of getting an even [#permalink]  21 Feb 2012, 01:46
I have re-read my posts and I think it's clear now.

Quote:
why the probability of getting 'four' on both dices is 1/36 and not 1/18? Why don't we make a difference between 4 on die1 and four on die?

This is because we fix dices one and two.

Quote:
A 5 meter long wire is cut into two pieces. 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 is cut at an arbitrary point?

This is because we can cut the wire from both ends. When we fix the ends, we can cut 1 m from the left, or we can cut 1 m from the right end. Both options are different since we have fixed the ends.

Quote:
When calculating probability, how should we know when to count the same instances and when not?

We don't count twice the same instances of the fixed "property" (don't know how to call that). But if two fixed properties (e.g., two dices: die_1 = property_one, die_2 = property_two) yield the same result by taking various values, we need to count those options (as in the above example with dices producing the sum of 8).

Bunuel, does the above make sense?
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4227

Kudos [?]: 41005 [0], given: 5654

Re: Two dice are tossed once. The probability of getting an even [#permalink]  21 Feb 2012, 03:20
Expert's post
nonameee wrote:
I have re-read my posts and I think it's clear now.

Quote:
why the probability of getting 'four' on both dices is 1/36 and not 1/18? Why don't we make a difference between 4 on die1 and four on die?

This is because we fix dices one and two.

Quote:
A 5 meter long wire is cut into two pieces. 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 is cut at an arbitrary point?

This is because we can cut the wire from both ends. When we fix the ends, we can cut 1 m from the left, or we can cut 1 m from the right end. Both options are different since we have fixed the ends.

Quote:
When calculating probability, how should we know when to count the same instances and when not?

We don't count twice the same instances of the fixed "property" (don't know how to call that). But if two fixed properties (e.g., two dices: die_1 = property_one, die_2 = property_two) yield the same result by taking various values, we need to count those options (as in the above example with dices producing the sum of 8).

Bunuel, does the above make sense?

I'm not sure that I understand completely the last part of your post, though it seems that you got the main point.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4227

Kudos [?]: 41005 [0], given: 5654

Re: Two dice are tossed once. The probability of getting an even [#permalink]  07 Jun 2013, 06:03
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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

_________________
Current Student
Status: Waiting
Joined: 11 Dec 2012
Posts: 77
Location: Bahrain
Concentration: Healthcare, General Management
GMAT 1: 640 Q49 V24
GMAT 2: 720 Q49 V40
WE: Sales (Other)
Followers: 4

Kudos [?]: 48 [0], given: 144

Re: Probability - tossing two dice [#permalink]  21 Jun 2013, 01:38
Bunuel wrote:
2. The probability of getting a total of 8 is 5/6^2, as there are 5 different favorable scenarios: (2,6), (6,2), (3,5), (5,3) and (4,4);

Dear Bunuel, my question pertains to the quoted text.

My reasoning to get sum 8 is:
Select any 5 numbers from first dice ie. probability: 5/6
To make the sum 8, only a unique number is to be chosen from 2nd dice. Hence the probability of selecting 1 number in second dice is : 1/6
Probability for sum 8 is 5/6^2. However I multiplied this number by 2 since you can perform the same task by selecting the second dice first and choosing a corresponding unique value in 1st dice.
Net probability is 5*2/6^2, but i believe this is wrong. Please let me know under what situations do we employ my understanding. Sorry if it is a silly question. Thank you for your time.
_________________

--
Piyush Jain

SVP
Joined: 06 Sep 2013
Posts: 2036
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 24

Kudos [?]: 294 [0], given: 354

Re: Two dice are tossed once. The probability of getting an even [#permalink]  23 Apr 2014, 05:15
I've done other problems in which the answer would simply come out from

1/2 + (1/2)(5/36)

That is first probability that we get an even number = 1/2
Second probability that we DON'T get an even number * Probability that we get a sum of 8 = (1/2)*(5/36)

Answer should be sum of both

Could someone please clarify why this approach is NOT valid?
Thanks!
Cheers
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4767
Followers: 296

Kudos [?]: 52 [0], given: 0

Re: Two dice are tossed once. The probability of getting an even [#permalink]  01 May 2015, 01:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Two dice are tossed once. The probability of getting an even   [#permalink] 01 May 2015, 01:44
Similar topics Replies Last post
Similar
Topics:
6 fair dice are tossed. What is the probability that at 13 09 Oct 2007, 11:47
6 fair dice are tossed. What is the probability that at 7 08 Oct 2007, 11:25
In tossing 4 fair dice, what is the probability of tossing, 10 27 Oct 2005, 17:56
6 fair dice are tossed. What is the probability that at 2 16 Oct 2005, 17:45
1) Two dice, each numbered 1 to 6, are tossed. Find the 3 05 Oct 2005, 19:29
Display posts from previous: Sort by

# Two dice are tossed once. The probability of getting an even

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.