F.5 MATHS probability

2010-12-15 2:58 pm

1. There are two bags of snooker balls. In each bag, there are four snooker balls as shown below:

Bag A:2,4,7,7
Bag B:1,4,4,4
(a) If a ball is drawn at random from each bag, find the probability that(i) both balls are of even numbers;(ii) two balls are different.(iii) the sum of the numbers is 8;(iv) the product of the numbers is even.
(b) A ball is drawn from each bag for exchange. Find the probability that each of both bags have two balls of the number ‘4’ after exchange.

回答 (1)

用戶25975

2010-12-15 4:43 pm

✔ 最佳答案

a) i) P(Even from A) = 1/4

P(Even from B) = 3/4

Thus, P(Both even) = 1/4 x 3/4 = 3/16

ii) There are 2 possibilities:

I) 4 from A and 1 from B, with prob. = 1/4 x 1/4 = 1/16
II) Not 4 from A and any from B, with prob. = 3/4

So P(Diff) = 1/16 + 3/4 = 13/16

iii) There are 2 possibilities:

I) 4 from A and 4 from B, with prob. = 1/4 x 3/4 = 3/16
II) 7 from A and 1 from B, with prob. = 1/2 x 1/4 = 1/8

So (sum is 8) = 3/16 + 1/8 = 5/16

iv) The product will be even if the drawn nos. are NOT both odd.

So P(both odd) = 1/2 x 1/4 = 1/8

Hence P(Product is even) = 1 - 1/8 = 7/8

b) To mak both bags have two balls of no. 4 after exchange, a ball NOT 4 should be drawn from A and a ball 4 should be drawn from B, with prob.

3/4 x 3/4 = 9/16

參考: 原創答案

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