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not understanding the answer

by emf_jay » Sat Mar 24, 2012 3:43 am
Plz Explain...
When a certain coin is flipped, the probability that it will land on heads is 1/2 and the probability that it will land on tails is 1/2. if the coin is flipped 3 times, what is the probability that all 3 results are the same ?? A. 1/8 B. 1/4 C. 3/8 D. 1/2 E. 7/8
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by coolhabhi » Sat Mar 24, 2012 4:40 am
The probability that it will be All Heads (HHH) or All Tails (TTT) is:
{(1/2)*(1/2)*(1/2)} + {(1/2)*(1/2)*(1/2)}
=>1/8 + 1/8
=>1/4
so B

Since getting a head or tail probability is 1/2.

Another way is to list down all the possibilities:
HHH
HHT
HTH
HTT
TTT
THT
TTH
THH

In these we have two favourable results are HHH and TTT. So the probability is 2/8
i.e., 1/4.
so B
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by GMATGuruNY » Sun Mar 25, 2012 2:20 am
emf_jay wrote:Plz Explain...
When a certain coin is flipped, the probability that it will land on heads is 1/2 and the probability that it will land on tails is 1/2. if the coin is flipped 3 times, what is the probability that all 3 results are the same ?? A. 1/8 B. 1/4 C. 3/8 D. 1/2 E. 7/8
The FIRST flip is irrelevant: the result can be heads or tails.
All that matters is what happens on the SUBSEQUENT flips.

P(2nd flip is the same as the first) = 1/2.
P(3rd flip is the same as the first 2 flips) = 1/2.
Since we want both events to happen, we multiply the fractions:
1/2 * 1/2 = 1/4.

The correct answer is B.
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