The lifetime in hours Y of an electronic component is a rand

The lifetime (in hours) Y of an electronic component is a random variable with its density function given by f_y (y) = {1/100 e^-y/100; y>0 Three of these components operate independently in a piece of equipment. The equipment fails if at least two of the components fail. Find the probability that the equipment will operate for at least 200 hours without failure.

Solution

F(y) = 1 - e^( -y / 100)

p [ lifetime > 200 hours ] = 1 - ( 1 - e^( - 200 / 100 ) ) = e^(-2)