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.