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# If four fair coins are tossed, what is the probability of

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SVP
Joined: 17 Jun 2008
Posts: 1504
If four fair coins are tossed, what is the probability of [#permalink]

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24 Sep 2008, 01:54
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If four fair coins are tossed, what is the probability of all four coming up heads?

A. 1/4
B. 1/6
C. 1/8
D. 1/16
E. 1/32

I tried to solve the above question as below.....what am I doing wrong?

favorable outcome of all four coming up heads = 4.
Total possible outcome = 2*2*2*2

Hence, probability = 4/16 = 1/4.

Alternatively, probability of getting head = 1/2
Hence, total probability = 1/2*1/2*1/2*1/2 = 1/16.
Manager
Joined: 24 Apr 2008
Posts: 160

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24 Sep 2008, 02:55
1
KUDOS
The sum of 4 is incorrect.

The event of all heads can occur only once = 1 and not 4
The denominator is as mentioned: 16

hence 1/16 sud be the OA.
SVP
Joined: 17 Jun 2008
Posts: 1504

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24 Sep 2008, 03:55
Thanks iamcartic. My silly mistake. I should have used 4C4.
VP
Joined: 30 Jun 2008
Posts: 1019

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24 Sep 2008, 05:08
The probability of getting exactly r results out of n coin-flips is:
$$nCr/2^n$$

so the probability of getting exactly 4 heads out of 4 flips is $$4C4/2^4$$ = 1/16
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Re: PS: Probability   [#permalink] 24 Sep 2008, 05:08
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