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As in Section 6.3, Exercise 5 and Section 6.4, Exercise 5, the sample space is S = {0, 1, 2, 3, 4}, Pr({0}) = 0.2, Pr({1}) = 0.3, Pr({2}) = 0.4, Pr({3}) = 0.1, Pr({4}) = 0.0, A = {0, 1, 2}, and B = {0, 2, 4).
Check whether the above event is independent by checking three equations:
Pr(A) = Pr(A | B) A is independent of B
Pr(B) = Pr(B | A) B is independent of A
Pr(A n B) = Pr(A)Pr(B). The multiplication rule
Do you ever find a case where only one or two of these equations is satisfied?
Jorge has three kids who spotted a Claw machine with toys they want. In stores the toys costs $10 each, but each play on the claw only costs $1. The probability of Jorge winning a game on the Claw is 0.12. Should he use the Claw to get the toys (he needs one toy per kid), or does he expect it to be cheaper to buy them in the stores?
