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# probability question

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Joined: 05 Apr 2013
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07 May 2013, 01:59
Hi,
I am stuck at a very basic probability question.
The problem statement -
If a fair coin is flipped twice what is the probability that heads will appear in either the first flip or the second flip?

This is my take on this problem.
If a coin is tossed twice below will be the different combinations that are likely to happen-

TT,TH,HT,HH.
So there are 4 possible combinations.SO the probability that heads will appear either in first or in second flip will be 2/4 = 1/2.

However if I try to solve the problem with the help of OR probability I am getting a different answer.

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

The probability that heads will appear in the first flip is 1/2.The probability that heads will appear in the seocnd flip is 1/2.and the probability that heads will appear in both flips is 1/2*1/2 = 1/4.

Therefore P(H1 or H2) =P(H1) + P(H2) - P(H1 and H2) = 1/2 + 1/2 - 1/4 = 3/4.

Can someone tell me why is there a difference in answer.Am I missing something here?
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Posts: 7377
Location: Pune, India
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08 May 2013, 08:42
chhandita wrote:
Hi,
I am stuck at a very basic probability question.
The problem statement -
If a fair coin is flipped twice what is the probability that heads will appear in either the first flip or the second flip?

This is my take on this problem.
If a coin is tossed twice below will be the different combinations that are likely to happen-

TT,TH,HT,HH.
So there are 4 possible combinations.SO the probability that heads will appear either in first or in second flip will be 2/4 = 1/2.

However if I try to solve the problem with the help of OR probability I am getting a different answer.

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

The probability that heads will appear in the first flip is 1/2.The probability that heads will appear in the seocnd flip is 1/2.and the probability that heads will appear in both flips is 1/2*1/2 = 1/4.

Therefore P(H1 or H2) =P(H1) + P(H2) - P(H1 and H2) = 1/2 + 1/2 - 1/4 = 3/4.

Can someone tell me why is there a difference in answer.Am I missing something here?

"what is the probability that heads will appear in either the first flip or the second flip"

means what is the probability that heads will appear in first of second or BOTH flips.
Hence 3 of the four cases - TH,HT,HH - satisfy our condition.

Another way to go about it is 1 - P(Both will be tails) = 1 - 1/4 = 3/4

Formally, 'either A or B' means it must be at least one of A and B. It can be both too.
_________________

Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 23 May 2013 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: probability question [#permalink] ### Show Tags 23 May 2013, 07:34 I need to learn GMAT immediately. pls tell me which title will help more for me in this forum to learn GMAT. Thanks Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7377 Location: Pune, India Followers: 2289 Kudos [?]: 15136 [0], given: 224 Re: probability question [#permalink] ### Show Tags 03 Jun 2013, 21:51 reosjenkeri wrote: I need to learn GMAT immediately. pls tell me which title will help more for me in this forum to learn GMAT. Thanks First, you need to get the Official Guide 13th Edition and you need to take the diagnostic test in the book. If your performance is below par, you need to work on your basics from your high school books (or websites e.g. purplemath.com, khanacademy.org) till your performance comes up to average. If your performance is average or above, all you will need is a complete set of GMAT prep material. Go through the entire set and Official Guide. Thereafter, start taking practice tests. You can check out the details of the Veritas study material here: http://www.amazon.com/Veritas-Prep-Comp ... ritas+GMAT _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: probability question   [#permalink] 03 Jun 2013, 21:51
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