The following tabic of data obtained from www.bascball-almanac.com shows hit inf

Question

The following tabic of data obtained from www.bascball-almanac.com shows hit information for four players. Suppose that one hit from the tabic is randomly selected. Arc 'the hit being made by Hank Aaron" and "the hit being a double" independent events? No, because P(hit is by Hank Aaronlhit by a double) is not equal to P(hit by Hank Aaron) Yes, because P(hit is by Hank Aaronlhit is a double) = P(hit is a double) No, because P(hit is by Hank Aaronlhit is a double) is not equal to P(hit is a double) Yes, bccausc P(hit is by Hank Aaronlhit is a double) = P(hit is by Hank Aaron)

Explanation / Answer

If given event then following must be true:

P(hit is being made by Hank Aaronlhit and hit is a double) =P(hit is being made by Hank Aaronlhit) *P(hit is a double)

And by condition probabaility we have

P(hit is being made by Hank Aaronlhit by a double ) = P(hit is being made by Hank Aaronlhit and hit is a double) / P(hit is being made by Hank Aaronlhit ) = [P(hit is being made by Hank Aaronlhit) *P(hit is a double) ] / P(hit is being made by Hank Aaronlhit ) = P(hit is a double)

But from the given table we have

P(hit is a double) = 1577/ 12351

Condiitonal probabaility

P(hit is being made by Hank Aaronlhit by a double ) = 624 / 3771

That is following is not true:

P(hit is being made by Hank Aaronlhit by a double ) = P(hit is a double)

Hence, first option is correct.

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