14. Researchers at the University of Pennsylvania School of Medicine have determ

Question

14. 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 31% chance of becoming myopic before they are 16. Children who sleep in darkness have a 26% probability of becoming myopic. A survey indicates that 27% of children under 2 sleep with some light on. Find the proba- bility that a random child under 2 will become myopic before reaching 16 years old. Probability 15. Suppose that at UVA, 76% of all undergraduates are in the College, 10% are in Engineering, 7% are in Commerce, 3% are in Nursing, and 4% are in Architecture. In each school, the per-centage of females is as follows: 55% in the College, 25% in Engineering, 49% in Commerce, 87% in Nursing, and 35% in Architecture. If a randomly selected student is male, what is the probability that he's from the College? Probability

Explanation / Answer

14)

P(become myopic)=P(sleep in light on and become myopic)+P(sleep in dark and become myopic)

=0.27*0.31+(1-0.27)*0.26=0.2735

15)

P(male)=P(in college and male)+P(in Engg and male)+P(in commerce and male)+P(in nursing and male)+P(in Arch, and male)

=0.76*(1-0.55)+0.1*(1-0.25)+0.07*(1-0.49)+0.03*(1-0.87)+0.04*(1-0.35)=0.4826

hence P(from college|male)=P(in college and male)/P(male)=0.76*(1-0.55)/0.4826 =0.7087

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