Question

Researchers at the University of Pennsylvania School of Medicine have determined that children under 2 years old who sleep with the lights on have a 36% chance of becoming myopic before they turn 16. Children who sleep in darkness have a 21% chance of becoming myopic before they turn 16. A survey indicates that 28% of children under 2 sleep with some light on. If a randomly selected child under 16 is myopic, what is the probability that he/she slept with the light on before they turned 2?

Answer 1

P(M|L)=.36
P(M|L^c)=.21
P(L)=.28
P(L^c)=.72
P(M|L)P(L)+P(M|L^c)P(L^c)
.36*.28+.21*.72
.252
Baye's Rule

Answer 2

m/p=236