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Charles flips a coin four times.  What is the probability that he gets a 3-1 split?  (3 heads and 1 tail, or 1 head and 3 tails)

 Jul 2, 2020
 #1
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You can do this just by listing the ways:

H-H-H-T  =  (½)·(½)·(½)·(½)  =  1/16

H-H-T-H  =  (½)·(½)·(½)·(½)  =  1/16

H-T-H-H  =  (½)·(½)·(½)·(½)  =  1/16

T-H-H-H  =  (½)·(½)·(½)·(½)  =  1/16

T-T-T-H  =  (½)·(½)·(½)·(½)  =  1/16

T-T-H-T  =  (½)·(½)·(½)·(½)  =  1/16

T-H-T-T  =  (½)·(½)·(½)·(½)  =  1/16

H-T-T-T  =  (½)·(½)·(½)·(½)  =  1/16

 

Adding the individual results give ½

There is another way, using combinations ...

 Jul 2, 2020
 #2
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As geno3141 says, here is another way:

 

4! / [3!*1!*2^4] * 2 =48 / 96 = 1 / 2

 Jul 2, 2020

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