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# We flip a fair coin 10 times. What is the probability that we get heads in exactly 8 of the 10 flips?

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We flip a fair coin 10 times. What is the probability that we get heads in exactly 8 of the 10 flips?

May 28, 2019

#1
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We have a binomial probability

C(10, 8)  * (.5)^8 * (.5)^2  = 45 / 1024  ≈  4.4%

May 28, 2019
#2
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We can also represent these using combinations.

We have to find the value of $$\binom{10}{8}.$$

A quicker way is to recognize Pascal's triangle, and this is the tenth row, and the sum is $$2^{10}=1024.$$ Thus, the answer is, $$\frac{\binom{10}{8}}{1024}=\boxed{\frac{45}{1024}}.$$

May 28, 2019
#3
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THX, AZSUN  !!!!

CPhill  May 28, 2019