Permutation and Combination 2

2011-01-18 1:21 am
12. A pair of fair dice is tossed. Find the probability of getting
(a) a total of 8;
(b) at most a total of 5.

13. In a poker hand consisting of 5 cards, find the probability of holding
(a) 3 aces;
(b) 4 hearts and 1 club.

14. Prove that
P(A' and B') =1+ P(A and B) - P(A) - P(B)
更新1:

13a 果度我想問點解係(52-4)C2而唔係(52-3)C2??

回答 (3)

2011-01-18 3:28 am
✔ 最佳答案
12a)A total of 8 cases including :
(2,6) (3,5) (4,4) (5,3) (6,2) , 5 cases.There are 6x6 = 36 cases.P(A total of 8) = 5/36
b)At most a total of 5 cases including :
(1,4) (2,3) (3,2) (4,1)
(1,3) (2,2) (3,1)
(1,2) (2,1)
(1,1)
, 10 cases.P(At most a total of 5) = 10/36 = 5/18
13a)(4C3) * (52 - 4)C2 / 52C5= 94/54145
b)13C4 * 13C1 / 52C5= 143/39984
14)P(A' and B')= (1 - A)(1 - B)= 1 + AB - A - B= 1+ P(A and B) - P(A) - P(B)


2011-01-17 23:02:51 補充:
如果 52 - 3 就包含了另一隻A,把4條A也計了,不行啊。

2011-01-17 23:12:40 補充:
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