Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.

n=10, p=0.5, x=4

p(4)

​(Do not round until the final answer. Then round to four decimal places as​ needed.)

Answer 1

P(4) =p(x=4) = 0.205078

Explanation:

Explanation:-

The probability of x successes in the n independent trials of the experiment.

Given n=10, p=0.5,

By using Binomial distribution

`P(X =x) = n_{C_(x) } p^(x) q^(n-x)`

Given the p = 0.5

q=1-p =1-0.5=0.5

`P(X =4) = 10_{C_(4) } (0.5)^(4) (0.5)^(10-4)`

we will use formula

`n_{C_(r) } = (n!)/((n-r)!r!)`

`10_{C_(4) } = (10!)/((10-4)!4!)=(10X9X8X7X6!)/(6!4!) =(10X9X8X7)/(4X3X2X1) =210`

`P(X =4) = 210 (0.5)^(4) (0.5)^(10-4)`

`P(X =4) = 210 (0.5)^(4) (0.5)^(6)`

on calculation, we get

P(X=4) = 0.205078