Question

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is
A. (1) red
B. (2) not red
C. (3) either red or white.
D.

Answer 1

Correct Answer - A::B::C
The sample space
`S={R_(1),R_(2),R_(3),W_(1),W_(2),W_(3),G_(1),G_(2),G_(3)}`
`thereforen(S)=9.`
A is the event that the ball picked up is a red ball. Now there are three red balls out of 9 balls.
`thereforeA={R_(1),R_(2),R_(3)}`
`thereforen(A)=3.`
`P(A)=(n(A))/(n(S))=(3)/(9)=(1)/(3).`
B is the event that the ball picked up is not a red ball,i.e.a ball picked up is either white or green.
There are 3+3 =6 balls (white+green ) out of the 9 balls.
`thereforeB={W_(1),W_(2),W_(3),G_(1),G_(2),G_(3)}`
`thereforen(B)=6.`
`P(B)=(n(B))/(n(S))=(6)/(9)=(2)/(3)`
C is the event that the ball picked up is either red or white.
There are 3+3=6 balls which are either red or white.
`thereforeC={R_(1),R_(2),R_(3),W_(1),W_(2),W_(3)}`
`thereforen(C)=6.`
`P(C)=(n(C))/(n(S))=(6)/(9)=(2)/(3).`