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Chapter 3: 3.2 (page 97)
If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is ? Compute for all values of between and
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Considerurns. An urn containswhite and red balls, an urn contains white and 4 red balls and urn contains white and red balls. If ball is selected from each urn, what is the probability that the ball chosen from urn was white given that exactly white balls were selected?
An engineering system consisting of n components is said to be a -out-of-system if the system functions if and only if at least of the components function. Suppose that all components function independently of one another.
(a) If the ith component functions with probability, compute the probability that a -out-of-system functions.
(b) Repeat part (a) for a -out-of-
system
In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) the probability that a randomly selected family owns both a dog and a cat? (b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?
In Problem 3.66a, find the conditional probability that relays and are both closed given that a current flows from to .
Fifty-two percent of the students at a certain college are females. Five percent of the students in this college are majoring in computer science. Two percent of the students are women majoring in computer science. If a student is selected at random, 铿乶d the conditional probability that
(a) the student is female given that the student is majoring in computer science;
(b) this student is majoring in computer science given that the student is female
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