Question

Q1) Two balls are randomly selected without replacement from a box containing three black balls numbered 1, 2, 3 and two white balls numbered 4 and 5. Assuming that all outcomes are equally likely. Find out the probabilities of following events. a) Probability that the color of second ball is white. b) Probability that the color of second ball is black. c) Probability that both balls are black. d) Probability that both balls are white.

Answer 1

`|\Omega|=5\cdot4=20`

a)

`|A|=3\cdot2+2\cdot1=8\\\\P(A)=(8)/(20)=(2)/(5)`

b)

`|A|=3\cdot2+2\cdot3=12\\\\P(A)=(12)/(20)=(3)/(5)`

c)

`|A|=3\cdot2=6\\\\P(A)=(6)/(20)=(3)/(10)`

d)

`|A|=2\cdot1=2\\\\P(A)=(2)/(20)=(1)/(10)`