probability

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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)

Guest Jul 2, 2020

geno3141 · Answer 1 · 2020-07-02T06:57:59

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 ...

Guest · Answer 2 · 2020-07-02T08:53:12

As geno3141 says, here is another way:

4! / [3!*1!*2^4] * 2 =48 / 96 = 1 / 2