Is. What is the probability of 30. We roll a pair of dice three times. Find the

Question

Is. What is the probability of 30. We roll a pair of dice three times. Find the probability that a g all even total exactly once? total of five is rolled exactly twice. The editors of Auto Web have evaluated several (E)juropean and J)apanese crossovers and given them either a (H)igh or (A)verage safety rating. The probability tree summarizes the results of the study. If a car from the study is selected randomly, find the prob- abilities indicated in Exercises 31-34 e) 0.65 H ume that e desired 0.40 0.35A ent. 0.75 0.60 a non- 0.25A de 32. P(H E) 34. P(H) 31. P(AIJ) andard 33. P(EnA) In Exercises 35-40, an experiment and two events are given. Determine if the events are independent or dependent. 35. A penny and a nickel are flipped; "head on the penny" and tail on the nickel." 36. Two dice (one red, one green) are rolled; "less than three on with- "the the red" and 'two on the green." , stond lard 52 card deck:

Explanation / Answer

SOLUTION FOR Q33

P(E A)

= P(A E)

= P(A/E) x P(E) [by definition of conditional probability]

Now, from the given probability diagram, probability that the editors of Auto Web will choose a European crossover is P(E) = 0.4. Once a European crossover is chosen, the chances of it getting an average rating is P(A/E) = 0.35. So,   

P(A/E) x P(E) = 0.35 x 0.4 = 0.14. Thus,

P(E A) = 0.14 ANSWER

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