Suppose that the genders of the three children of a family are soon to be revealed....

  

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Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (If necessary, consult a list.of.formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes Probability BBB BBG BGB BGG GBB GBG|GGB GGG Event X: The first child is a boy Event Y: Exactly two children are girls Event X and Y: The first child is a boy and exactly tvwo children are girls 日 (b) Suppose the first child is a boy. (That is, Event X occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event Y. Then, enter the probability that Event Y occurs given that Event X occurs. Outcomes given the first child is a boy Probability BBB BBG BGB BGG Event Y: Exactly two children are girls (c) Give the following probabilities and select the correct option below. P(X and Y) P(X) P(Y|X) = P(X and Y) • P(Y\x) P(X) Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (If necessary, consult a list.of.formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes Probability BBB BBG BGB BGG GBB GBG|GGB GGG Event X: The first child is a boy Event Y: Exactly two children are girls Event X and Y: The first child is a boy and exactly tvwo children are girls 日 (b) Suppose the first child is a boy. (That is, Event X occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event Y. Then, enter the probability that Event Y occurs given that Event X occurs. Outcomes given the first child is a boy Probability BBB BBG BGB BGG Event Y: Exactly two children are girls (c) Give the following probabilities and select the correct option below. P(X and Y) P(X) P(Y|X) = P(X and Y) • P(Y\x) P(X)