Answer to Question #118370 in Statistics and Probability for Nickey Namwiha

Question

determined that
children under 2 years old who sleep with the light on have a 36 % chance of becoming myopic
before they are 16. Children who sleep in darkness have a 21 % chance of becoming myopic. A
survey indicated that 28% of children under 2 sleeps with some light on. Find the probability
that child under 16 is myopic.

Answer 1

The children under 2 years old  - 28%, sleep with the light - 36% chance of becoming myopic .

Children who sleep in darkness - 100%-36%=64% , children who sleep in darkness have a 21 % chance of becoming myopic .

According to Baess's formula

$p=\frac{P(H_1)P(A/H_1)}{P(H_1)P(A/H_1)+P(H_2)P(A/H_2)}$

$P(H_1)=0.28\\P(A/H_1)=0.36\\ P(H_2)=0.64\\P(A/H_2)=0.21$

$p=\frac{0.28\cdot0.36}{0.28\cdot0.36+0.64\cdot0.21}=\frac{0.1008}{0.2352}=0.4286$

The probability that child under 16 is myopic 43%.