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 =
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.