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The probability is 1/2 that a certain coin will turn up head

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The probability is 1/2 that a certain coin will turn up head [#permalink] New post 26 Dec 2012, 05:53
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The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16
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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 26 Dec 2012, 05:59
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Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

Answer: D.
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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 04 Jan 2013, 17:27
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Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8
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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 16 Sep 2013, 11:09
caioguima wrote:
Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8


Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2.
According to my understanding, the prob of head is 1/2 and tail is 1/2.
So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3?
Kindly clarify.
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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 16 Sep 2013, 11:17
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abhinaya wrote:
caioguima wrote:
Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8


Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2.
According to my understanding, the prob of head is 1/2 and tail is 1/2.
So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3?
Kindly clarify.


The point is that two heads and a tail can occur in three ways: HHT, HTH, THH. The probability of each case is 1/2*1/2*1/2.

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

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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 20 Nov 2013, 04:41
Bunuel wrote:
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

Answer: D.


Bunuel, would you mind explaining how you find the power to which you have to raise? What if e.g. there is a bag with three marbles, blue, red and yellow. Now the question is e.g. "What is the probabilty to get a blue marble on at least 1 try if you try 4 times" (putting the marbles back all the time).

Would it be P(at least 1 blue marble) = 1 - P(none blue) = 1 - (2/3)^4 ??

Thanks for your explanation!
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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 20 Nov 2013, 04:51
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unceldolan wrote:
Bunuel wrote:
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

Answer: D.


Bunuel, would you mind explaining how you find the power to which you have to raise? What if e.g. there is a bag with three marbles, blue, red and yellow. Now the question is e.g. "What is the probabilty to get a blue marble on at least 1 try if you try 4 times" (putting the marbles back all the time).

Would it be P(at least 1 blue marble) = 1 - P(none blue) = 1 - (2/3)^4 ??

Thanks for your explanation!


Yes, that's correct, the power must be the number of tries.

For the original question: P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2*1/2*1/2)= 1 - (1/2)^3 = 7/8.

For your example: P(at least 1 blue) = 1 - P(no blue) = 1- (2/3*2/3*2/3*2/3) = 1- (2/3)^4.

Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The probability is 1/2 that a certain coin will turn up head [#permalink] New post 20 Nov 2013, 05:35
ok great :) thank you!
Re: The probability is 1/2 that a certain coin will turn up head   [#permalink] 20 Nov 2013, 05:35
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