Solve the following problems 1 Suppose the fraction of under

Solve the following problems: 1. Suppose the fraction of undergraduate students who smoke is 15% and the fraction of graduate students who smoke is 23%. If one-fifth of the college students are graduate students and the rest are undergraduates. what is the probability that a student who smokes is a graduate student? a. Given the information in part (a), is a randomly chosen college student more likely to be a graduate or undergraduate student? b. b. Repeat part (b) assuming that the student is a smoker. 2. A certain pickup truck comes equipped with either an automatic or a manual transmission. and the truck is available in one of four colors. Relevant probabilities for various combinations of transmission type and color are given in the accompanying table. Let A = (automatic transmission). B = {black}. and C = {white}. a. Calculate P(A). P(B), and P(A B). b. Calculate both P(AIB) and P(BIA). and explain in context what each of these probabilities represents.

Solution

1>

Notations: Graduate(G), Not Graduate(NG),Smokes(S)

P(G)=1/5

P(S/G)=0.23

P(NG)=4/5

P(S/NG)=0.15

So, P(G/S) = P(G and S) / P(S)

= (0.23/5) / (0.6/5 + 0.23/5)

=0.28

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a> A random student chosen is more likely to be a undergraduate as there are 80% of the people who are undergraduates.

b> A random student chosen who smokes is more likely to be a undergraduate as there are only 28% of the smokers who are graduates as calculated by us above

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2>

a>

P(A) = 0.13 + 0.10 + 0.11 + 0.11 = 0.45

P(B) = 0.11 + 0.15 = 0.26

P(A and B) = 0.11

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b>

P(A|B) = P(A and B) / P(B) = 0.11 / 0.26 = 0.42

P(B|A) = P(A and B) / P(A) = 0.11 / 0.45 = 0.24