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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
avatar+109355 
+1

We have a binomial probability

 

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

 

 

cool cool cool

 May 28, 2019
 #2
avatar+191 
+1

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
avatar+109355 
0

THX, AZSUN  !!!!

 

 

cool cool cool

CPhill  May 28, 2019

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