Question

A piece of electronic equipment is built with 3 cooling fans. The equipment will function only if at least 2 of the 3 fans are working. The lifetimes of the fans are subject to forces of mortality that are independent, constant, and identical. The force of mortality is equal to 0.098. Calculate the probability that the electronic equipment will work for at least 5 years. (Ans 0.66608)

Answer 1

0.66608

Explanation:

Equipment = 3 fans

Mortality = 0.098

We are required to find probability that equipment gets to work for 5years

The question says forces of mortality is constant and also equal to 0.098

To calculate p(x>5)

We will do this by calculating exponentially

e^-0.098x5

= 0.612626394

Probability that at least 2 fans out of 3 are working

3(0.612626394)²+(1-0.612626394)+(0.612626394)³

= 1.1259333x0.3873736+0.2299255

= 0.6660823470

This is approximately

0.6608

this is the probability that the equipment will work for at least 5years