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

Answer:

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

Step-by-step 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

$n_{C_{r} } = \frac{n!}{(n-r)!r!}$

$10_{C_{4} } = \frac{10!}{(10-4)!4!}=\frac{10X9X8X7X6!}{6!4!} =\frac{10X9X8X7}{4X3X2X1} =210$

$P(X =4) = 210 (0.5)^{4} (0.5)^{10-4}$

$P(X =4) = 210 (0.5)^{4} (0.5)^{6}$

on calculation, we get

P(X=4) = 0.205078