Probability problem...Help required.......?

Question

There are 6 black and 10 white balls in a basket.

(1)While shaking the basket, each ball has equal chance to collide with the other. What is the probability of a white ball to collide with a black ball twice?

(2) If 6 black balls are kept in two packets such that each packet contains 3 black balls and those packets along with the 10 white balls are then placed in the basket, what is the probability of one white ball colliding with the same black ball packet twice?

Philip · Accepted Answer

(1)The number of ways for a white ball to collide with a black ball is 10*6 = 60
The number of ways for any 2 balls to collide is 16C2 = 120
So the probability of a white ball colliding with a  black ball is 60/120 = 0.5
For this to happen twice p = 0.5*0.5 = 0.25

(2) Essentially this is the same as 10 white and 2 black.
The number of ways for a white ball to collide with a black ball is 10*2 = 20
The number of ways for any 2 balls to collide is 12C2 = 66
So the probability of a white ball colliding with a black ball is 20/66 =10/33
For this to happen twice p = 10/33*10/33 = 100/1089 = .0918

Probability problem...Help required.......?

1 Antwort