probability

[匿名]

2013-02-14 7:49 pm

1) Betty has 10 gold medals band 7 silver medals, and Monica has 9 gold medals amd 8 silver medals. If all of their medals are put into a box, and five medals are randomly selected from it, find the probabilities of the following events happening.

a) Four gold medals are selected, given that all medals are from Betty.
b) All medals are from Betty, given that four gold medals have been selected.

2) There are 20 boys and 15 girls in S6A, 18 boys and 18 girls in S6B. 3 students from each class are selected randomly to join a quiz. Find the probabilities of the following events happening.

a) All students selected are in the same sex.
b) At least 1 boy is selected from each class, and the numbers of boys selected from both classes are the same.

(Give your answers correct to 3 significant figures.)

Thanks

更新1:

Can someone help?? x_x

回答 (1)

用戶2053

2013-02-16 1:05 am

✔ 最佳答案

1a)P(Four gold medals are selected, given that all medals are from Betty)
= 10C4 * 7C1 / 17C5
= 105 / 442
b)P(All medals are from Betty, given that four gold medals have been selected)
= 10C4 * 7C1 / (19C4 * 15C1)
= 49 / 1938

2a) P(All students selected are in the same sex)
= (20C3 * 18C3 + 15C3 * 18C3) / (35C3 * 36C3)
= 0.0279
b)P(At least 1 boy is selected from each class, and the numbers of boys selected from both classes are the same)= 20C1 * 15C2 * 18C1 * 18C2 + 20C2 * 15C1 * 18C2 * 18C1 + 20C3 * 18C3
────────────────────────────────────────────────
35C3 * 36C3=
(5783400 + 7848900 + 930240) / 46731300= 0.312

👍 0 👎 0