i want EX 5.6 That said, we can state a rule for calculating \"and\" probabiliti
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i want EX 5.6
That said, we can state a rule for calculating "and" probabilities which is true within appropriate contexts. If it is appropriate within the context of a given problem, the probability of A and ? is the product of their individual probabilities. That is, P(A and B) = P(A)P(B) If a die is rolled twice, and the outcome is recorded after each roll. What is the probability of getting a 2 first and getting an even number second? What is the probability of getting two 3's? What is the probability of getting two 3's and getting two 4's? Adelle, Ben, and Christina are three friends who play tennis together regularly and who all aspire to be statisticians. Based on data they have collected over several years, it appears that the probability that Adelle will beat Ben is 0.6; the probability that Adelle will beat Christina is 0.55; and the probability Ben will beat Christina is 0.3. This weekend they will play a round-robin tournament. What is the probability Adelle will beat Ben and Christina? What is the probability Ben will win both of his matches? What is the probability that Christina will beat Ben, but lose to Adelle? What is the probability Adelle will lose both her matches? What is the probability Ben will win exactly one of his matches?Explanation / Answer
a) P = P(A) * P(B) = 0.6 * 0.55 = 0.33
b) P = (1 - 0.6)*0.3 = 0.4 * 0.3 = 0.12
c) P = 0.55 * (1 - 0.3) = 0.55 * 0.7 = 0.385
d) P = (1 - 0.6) * (1 - 0.55) = 0.4 * 0.45 = 0.18
e) P = 0.6 * 0.3 + (1 - 0.6)*(1 - 0.3) = 0.6*0.3 + 0.4*0.7 = 0.46
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