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

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Author:Amos Gilat
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Researchers have determined that children under 2 years old who sleep with the lights on have a 36% chance of becoming myopic (bad eyesight) before they are 16 years old. Children who sleep in darkness have a 21% chance of becoming myopic. A survey indicates that 28% of children under 2 years old sleep with some light on. Find the probability that a child under 16 years old is myopic.

 

Expert Solution
Step 1

From the given information,

Consider, A be the event that shows children under 2 years old sleep with light.

Ac is the event that  shows children under 2 years old sleep with darkness.

Let E be the event that shows child has myopic.

Thus,

PA=0.28PAc=1-PA=1-0.28          =0.72PE|A=0.36PE|Ac=0.21

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