Statistic question

Question

A local fire station has 3 fire engines operating independently. The probability that a specific engine is available when needed is 0.9.

(a) What is the probability that neither is available when needed?

(b)  What is the probability that at least one fire engine is available when needed?

Answer 1

The probability that a specific engine is NOT available is 1 - 0.9 = 0.1.

The probability that none of the engines are available, given they are operating independently is 0.1 * 0.1 * 0.1 = 0.001.

The probability that at least one fire engine is available is equal to 1 - probability none of the engines are available = 1 - 0.001 = 0.999.