Answer all correctly.

1A.10 The sports club Three quarters of the members of a sports club are adults, and one quarter are children. Three quarters of the adults, and three fifths of the children, are male. Half the adult males, and a third of the adult females, use the swimming pool at the club; the corresponding proportion for children of cither sex is four fifths. (a) Find the probability that a member of the club uses the swimming pool. (b) Find the probability that a member of the club who uses the swimming pool is male. (c) Find the probability that a member of the club is female. (d) Find the probability that a member of the club who uses the swimming pool is female. (e) Find the probability that a male user of the swimming pool is a child. (f) Find the probability that a member of the club who does not use the swimming pool is either female or an adult.1A.7 The fisherman Each Sunday a fisherman visits one of three possible locations near his home: he goes to the sea with probability , to a river with probability ), or to a lake with probability ]. If he goes to the sea there is an 80% chance that he will catch fish; corresponding figures for the river and the lake are 40% and 60% respectively. (a) Find the probability that, on a given Sunday, he catches fish. (b) Find the probability that he catches fish on at least two of three consecutive Sundays. (c) If, on a particular Sunday, he comes home without catching anything, where is it most likely that he has been? (d) His friend, who also goes fishing every Sunday, chooses among the three locations with equal probabilities. Find the probability that the two fishermen will meet at least once in the next two weekends. (Any assumptions you make in solving this problem should be clearly stated.)17. If a person is chosen at random from the island, what is the probability that they have blood type A and are from ethnic group 2? [5 pts] 18. Given that a person has blood type A, what is the probability that they are from ethnic group 1? [5 pts] Questions 19-20. John is playing a dice game in which he will roll two dice. If at least one of the dice is a 5 or 6, John wins. 19. What is the probability that John wins a game? [5 pts] 20. If John plays the game 5 times, what is the probability that he wins exactly 3 times? [5 pts]Questions 13-14. The cumulative distribution function is shown below for the random variable X. 0 0.20 05 x