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1. Given that P(A ∪ B)=5/9 and P(A ∩ B^' )=8/15, determine P(B). 2. A country...

1. Given that P(A ∪ B)=5/9 and P(A ∩ B^' )=8/15, determine P(B).

2. A country club has a membership of 500 members and operates facilities that include a swimming pool and a gymnasium. The club president would like to know how many members regularly use the facilities. A survey of the members indicates that 70% regularly use the swimming pool (S), 50% regularly use the gymnasium (G), and 5% use neither of these facilities regularly. Calculate the probability of the club members who use the facilities of the swimming pool and gymnasium P(S∩G).           

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