Combinatorics Olympiad Problem 3

Probability Level 2

What is the probability of obtaining exactly 3 heads if a fair coin is flipped 6 times? Express the answer as a decimal.

This problem is not original. It is roughly the level of difficulty of a BMO problem. This problem is part of this set .


The answer is 0.3125.

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4 solutions

Using Binomial Distribution, It can be easily seen that probability of winning is 20/64.

P(winning) = 6C3*1/2^6.

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Tanishq Varshney
Mar 18, 2015

its easy

6 C 3 1 2 6 = 20 64 ^{6}C_{3} \frac{1}{2^6}=\frac{20}{64}

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Applying the concept of Bernoulli trial, we have: C(6, 3) * (1/2)^3 * (1/2)^3 = 5/16 = 0.3125 :)

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Rahul Saxena
Mar 29, 2015

Did the same way.

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