Answer to Question #125120 in Statistics and Probability for Jack

Question

A Covid 19 testing machine at a testing centre breaks down an average of three times per year. Using an appropriate probability distribution formula, find the probability that during the next year, this machine will have;

i. exactly two breakdowns

ii. at most one breakdown

Answer 1

solution:

The number of successes in two disjoint time intervals is independent. The probability of a success during a small time interval is proportional to the entire length of the time interval

given : $\lambda$ = 3

Formula: P(X=x)= $\frac{\lambda ^{x}e^{\lambda }}{x!}$

part i)

Exactly two breakdowns

P(x=2)= $\frac{3 ^{2}e^{3 }}{2!}$ = 0.2240

Part ii)

At most one breakdown:

P(X$\leq$ 1)= P(X=0)+P(x=1)

=$\frac{3 ^{0}e^{3 }}{0!}$ + $\frac{3 ^{1}e^{3 }}{1!}$

=0.0498+0.1494

=0.1992