College Math

College Math Study Guide

9. d Solution: In this case, let event A be the people who eats healthy food and event B be the people who exercise regularly. Now, it is given that n(A) = 48, n(B’) = 65, thus, n(B) = 100-65 = 35, n(A∩B)=27 and n(A∩B)’ = 44 Let us draw a Venn diagram to understand the problem.

We have to find, P(B|A) = P(A∩B)/P(A) = 27/48 = 56% 10. c Solution: This is the problem of conditional probability. Let T be the event that tails has been tossed and W be the event that a white ball is drawn. We know that, Probability of drawing a white ball from urn 2, given that tails has been tossed =P(W|T) =3/15, Probability of drawing white ball from urn 1, when tails is not tossed = P(W/T’) = 5/12 The probability of tossing tail P(T)= probability of not tossing tail P(T’) = ½ To find: P((T|W) = P(T∩W)/ (W) Now, we know that: P(W|T) = P(W∩T)/P(T) Substituting the values, we get 3/15 = P(W∩T)/(1/2) P(W∩T) = 3/15 * ½ = 1/10

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