Lindsay D.

asked • 03/28/16

can someone help me with this probability question.

A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

So i figured that 29=512 but that is as far as i can get. Can someone please help me.


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Kenneth S. answered • 03/28/16

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There are 9C6 ways to get exactly 6 heads. The probability of this event is 84/512 = 21/128 ≈ 0.164 (Binomial distribution)
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Lindsay D.

I am having a hard time understanding this who binomial distribution. I dont understand where the 84 came from. I understand how you broke it down from 84/512 but i am really not sure how you figured out the 84. Could you help me understand binomial distribution it just does not make sense.
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03/28/16

Kenneth S.

The notation 9C6 means that you have 9 H's, from which you choose 6.  This is called a binomial coefficient--numbers that can be produced by Pascal's Triangle (of which you should have heard in Algebra II class), or by using the Combination Definition: nCr means from n things, choose r of them, and the formula is nCr = n!]r!(n-r)!].  That's where the 84 comes from.
 
To learn more on this topic, research Binomial Distribution and/or Bernoulli Trials.  It's related to the Binomial Theorem.
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03/28/16

Kenneth S.

Correcting a typo in my comment: nCr = n! / [r!(n-r)!]   
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03/28/16

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