Question

In a manufacturing plant that produces new computers, a 0.15 probability exists that a computer will be defective. if five computers are manufactured, what's the probability that all of them will be defective?

Answer 1

The probability that all of them will be defective is 0.0000759375

Explanation

The general Binomial Probability formula is....

$P= ^nC_{r}*p^r*(1-p)^n^-^r$, where p is the probability of success, n is the total number of trials and r is the desired numbers of trials.

Given, the probability that a computer will be defective is 0.15 , so p = 0.15

Five computers are manufactured and we need to find the probability that all of them will be defective. That means, n = 5 and r = 5

Now according to the above formula....

$P= ^5C_{5}*(0.15)^5*(1-0.15)^5^-^5 \\ \\ P= 1*(0.15)^5* (0.85)^0\\ \\ P=(0.15)^5 =0.0000759375$

So, the probability that all of them will be defective is 0.0000759375