The probability- @ 快遞百科

標題:

The probability?

發問:

The probability that in a single shot Peter hits a target is 1/4 and the probability that John hits the same target is 1/3. If each person shoots twice, what is the probability that the target will be hit exactly twice? answers:37/144 pls.

最佳解答:

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Target exactly hit twice, cases : 1. Peter hit twice and John does not hit at all 2. Peter hit once and miss one, John hit once and miss once total 4 cases, Peter hit 1st, miss 2nd , John hit 1st miss 2nd Peter miss 1st, hit 2nd, John hit 1st, miss 2nd Peter miss 1st hit 2nd, John miss 1st, hit 2nd Peter hit 1st, miss 2nd, John miss 1st, hit 2nd 3. Peter miss twice and John hit twice Case 1 Probability = (1/4)*(1/4)*(2/3)*(2/3) = 1/36 Case 2 Probability = 4 * (1/4)*(3/4)*(1/3)*(2/3) = 1/6 Case 3 Probability = (3/4)*(3/4)*(1/3)*(1/3) = 1/16 Total = 1/36 + 1/6 + 1/16 = 37 / 144

其他解答:

Probability: = (1/4)(1/4)(2/3)(2/3) + (3/4)(3/4)(1/3)(1/3) + (1/4)(3/4)(1/3)(2/3)(4) = (1/36) + (1/16) + (1/6) = (4 + 9 + 24) / 144 = 37/144