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中五數學-概率問題

發問:

1.Three dice are thrown.What is the probability that the sum of the three numbers is even if only one of the number is a "3"?2.A problem is solved independently by Alfred, Sam,Andrew.The probability that the problem can be solved by them are "4/7","1/3","3/5".find the... 顯示更多 1.Three dice are thrown.What is the probability that the sum of the three numbers is even if only one of the number is a "3"? 2.A problem is solved independently by Alfred, Sam,Andrew.The probability that the problem can be solved by them are "4/7","1/3","3/5". find the probability that (a) all three of them can solve the problem (b) exactly one of them can solve the problem (c) the problem can be solved (d) If one of them are selected randomly to solve the problem,find the probability that the problem can be solved.

最佳解答:

If the 3 appear at the first dice Then the possible combinations of the other two dices (1,2) (1,4) (1,6) (2,1) (2,5) (4,1) (4,5) (5,2) (5,4) (5,6) (6,1) (6,5) Similar for 3 appears at the second or third dice so total combinations 36 probability =36/216 =1/6 2 (a) probability=(4/7)(1/3)(3/5)=4/35 (b) probability =(4/7)(2/3)(2/5)+(3/7)(1/3)(2/5)+(3/7)(2/3)(3/5) =(16+6+18)/105 =40/105 =8/21 (c) the probability that the problem cannot solved =(3/7)(2/3)(2/5) =12/105 So the probability problem can be solved =1-12/105 =93/105 (d) in this case the probability problem cannot be solved =(1/3)(3/7+2/3+2/5) =[(45+70+42)/105](1/3) =157/315 So probability that the problem can be solved =158/315 Right?

其他解答:

problem is solved independently by Alfred, Sam,Andrew.The probability that the problem can be solved by them are "4/7","1/3","3/5". find the probability that7638E748CCC65837