Question

If there are 3 buckets, each with 3 balls: 1 red, 1 blue, and 1 white. If one ball is randomly selected from each bucket, what is the probability of:

a) getting exactly 2 white balls

b) getting at least 2 blue balls

c) getting 3 white balls

d) getting at least 1 red ball

Answer 1

a)as probability of white balls frm a bucket=(1/3)

getting exactly 2 white balls=³C₂(1/3)²*(2/3)¹ =2/9

b)

P(getting at least 2 blue balls)=P(2 blue balls )+P(3 blue balls)=³C₂(1/3)²*(2/3)¹ +³C₃(1/3)³*(2/3)⁰ =(2/9)+(1/27)=7/27

c)

P(getting 3 white balls)=³C₃(1/3)³*(2/3)⁰ =1/27

d)

P(getting at least 1 red ball)=1-P(no red ball)=1-(2/3)³ =19/27