probability 20pts

ICC*

2011-10-02 9:28 pm

1. In a game between A and B the chances of winning points are as follow:

A B
Chance of winning the first point: 3/5 2/5
Chance of winning if A won first point 2/3 1/3
Chance of winning if B won first point 1/2 1/2

a) Find the chance that A wins the first four points
b) each wins one of the first two points

Ans a. 8/45, b. 2/5
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2. A box contains four bad tubes and six good tubes. Two are drawn together, one of them is tested and found to be good.

a) what is the probability that the other is also good.
b) if the tubes are checked by drawing a tube at random, testing it and repeating the process (not replacing the tube tested) until all four bad tubes are located, what is the probaility that fourth bad tube will be found at the fifth test?

Ans a. 5/9
b. 2/105

回答 (1)

myisland8132

2011-10-02 9:43 pm

✔ 最佳答案

1(a) P(A wins the first four points)

= P(AAAA)

= (3/5)(2/3)(2/3)(2/3)

= 8/45

(b) P(each wins one of the first two points)

= 1 - P(AA) + P(BB)

= 1 - (3/5)(2/3) - (2/5)(1/2)

= 1 - 9/15

= 2/5

2(a) Since you know that one is good, the other one should be chosen from 9 tubes where 5 are good. So, the probability is just 5/9

(b) We should draw 3 bad tubes in the first four draw and the fifth draw should obtain the bad one.

So, probability

= C(4,3)C(6,1)/C(10,4) * 1/6

= 24/210 * 1/6

= 2/105

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