Mathematics: A factory purchased 15 machines. Each machine has 0.2 probability of breaking down. What is the probability of 1 machine breaking down?

- x - 5Step-by-step explanation:...

A factory purchased 15 machines. Each machine has

dudeper40

29.01.2022

The probability of one machine breaking down

P(X=1) = 0.13194

Step-by-step 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

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