4. Suppose there are 5 bowling balls which are identical except that one is magical and delivers, no matter what, a strike with probability 3/4. Suppose you get a strike 1 out of 4 times on average when using non-magical bowling balls. You select one of the 5 balls at random and send it down the lane.... (a) Give the probability that you get a strike. (b) Given that you got a strike, what is the probability you chose the magic bowling ball? (c) Suppose you choose a ball and with the same ball you get two strikes in a row. What is the probability that you chose the magic ball?

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