Please show work. Thank you! 05.ConditionalProbability 1: Problem 1 Prev Up Next
ID: 3303912 • Letter: P
Question
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05.ConditionalProbability 1: Problem 1 Prev Up Next (1 pt) 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 38% chance of becoming myopic before they are 16, Children who sleep in darkness have a 22% probability of becoming myopic. A survey indicates that 30% of children under 2 sleep with some light on. Find the probability that a random child under 2 will become myopic before reaching 16 years old. Probability =Explanation / Answer
Let,
ON denote lights are ON
OFF denote lights are OFF
M denote Myopic
NM denote Not Myopic
Now we are given ,
P(M|ON)= 0.38 ,that is given lights are ON 38% children will be myopic before 16 years of age
P(M|OFF)=0.22,that is given lights are OFF 22% children will be myopic before 16 years of age
P(ON) = 0.3,P(OFF) =1-P(ON) =0.7
Prob that a random child will become myopic is
P(ON)*P(M|ON)+P(OFF)*P(M|OFF) =0.3*0.38+0.7*0.22 = 0.268