Problem 36 Solution

Warning: This is just a quick explanation which assumes some knowledge of the exponential distribution and integral calculus.

The density function of the shorter lived life bulbs is f(x)=1/100 * e^-x/100.

The density function of the longer lived life bulbs is f(x)=1/200 * e^-x/200.

The probability of any given 100 hour bulb burning out first is the integral from 0 to infinity of (1/100)*e^-x/100*(e^-x/100>⁴*(e^-x/200)⁵ =

1/100 * integral e^-15x/200 =

(1/100)*(200/15)=2/15.

The probability that ANY of the 100 hour bulbs burn out first is five times this answer, or 10/15=2/3.

Michael Shackleford, A.S.A.