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 = 15, p = 0.3, X = 3
P(3)=0

Answer 1

Answer:

$P(x = 3) = 0.1700$

Explanation:

Given

$n = 15$

$p = 0.3$

Required

Determine P(x = 3)

This is calculated using:

$P(x) = ^nC_xp^x(1-p)^{n-x}$

So, we have:

$P(x = 3) = ^{15}C_3*0.3^3*(1-0.3)^{15-3}$

$P(x = 3) = ^{15}C_3*0.3^3*(1-0.3)^{12}$

$P(x = 3) = 455 *0.027*(0.7)^{12}$

$P(x = 3) = 455 *0.027*0.0138412872$

$P(x = 3) = 0.17004021325$

$P(x = 3) = 0.1700$