Question

A factory purchased 15 machines. Each machine has 0.2 probability of breaking down.

What is the probability of 1 machine breaking down?

Answer 1

The probability of one machine breaking down

P(X=1) = 0.13194

Explanation:

Step(i):-

Given sample size 'n' = 15

The probability of breaking down of each machine = 0.2

p = 0.2

q = 1-p = 1-0.2 = 0.8

Step(ii)

Let 'X' be the random variable in binomial distribution

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

The probability of one machine breaking down

`P(X=1) = 15_{C_(1) } (0.2)^(1) (0.8)^(15-1)`

On calculation , we get

P(X=1) = 15 ×(0.2)×(0.8)¹⁴

P(X=1) = 0.13194

Final answer:-

The probability of one machine breaking down

P(X=1) = 0.13194