Question

A fair coin is tossed 20 times. What is the probability of getting at most 18 heads??

Answer 1

`= 0.999979973`

Explanation:

`"The complementary event is easier to calculate."`
`"So we calculate the probability of getting more than 18 heads."`
`"This is equal to the probability of getting 19 heads, plus the"`
`"probability of getting 20 heads."`
`"We apply the binomial distribution."`

`P["19 heads"] = C(20,19) (1/2)^20`
`P["20 heads"] = C(20,20) (1/2)^20`

`"with"`
`C(n,k) = (n!)/((n-k)!k!)`
`"(combinations)"`

`=> P["19 or 20 heads"] = (20 + 1) (1/2)^20 = 21/1048576`

`=> P["at most 18 heads"] = 1 - 21/1048576`
`= 1048555/1048576`
`= 0.999979973`