F.5 Maths Probability

2009-12-25 2:36 am

1.One cards is drawn at random from each of the two decks of 52 playing cards.Find the probability that one card is an ace and the other card is a king.

2. Two packs of application forms are mixed together by accident. One pack contains 50 green forms, the other pack contains 30 white forms. If three forms are
chosen successively at random without replacement, find the probability that three forms are of different colours.

3.Two dice are thrown. Find the probability that the sum of the numbers is 6 if they are both odd.

回答 (1)

用戶2053

2009-12-25 3:23 am

✔ 最佳答案

1) P(one card is an ace and the other card is a king)
= P(AK) + P(KA)
= 4/52 * 4/52 + 4/52 * 4/52
= 2/169
2)P(three forms are of different colours)
= 1 - P(three forms are green) - P(three forms are white)
= 1 - 50/80 * 49/79 * 48/78 - 30/80 * 29/79 * 28/78
= 1 - 245/1027 - 203/4108
= 0.712025316
3) Both odd : 3*3 = 9cases
sum = 6 : 1+5 , 5+1 , 3+3 , 3 cases
P( the sum of the numbers is 6 if they are both odd) = 3/9 = 1/3

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