Question

A box contains 7 red, 3 green and 3 yellow balls. If two balls are drawn from the box, then what is the probability of getting

a) two red balls?

b) 1 red and 1 yellow balls?

c) non-red balls?

d) two green balls?

Answer 1

Let R, G and Y represent red, green and yellow balls respectively. Probabilities for selecting these balls are given by,

$p(R)=7/13$

$p(G)=3/13$

$p(Y)=3/13$

Also define S as the sample space obtained by selecting 2 balls at random then,

$S=\{RR,RG,RY,GR,GG,GY,YR,YG,YY\}$

a.

Probability that both balls selected are red $\{RR\}$ is given by,

p(both balls are red)=7/13*6/12=42/156=7/26

b.

Probability that the balls selected includes 1 red and 1 yellow ball $\{RY, YR\}$ is given as,

p(1 red and 1 yellow balls)=(7/13*3/12)+(3/13*7/12)=42/156=7/26

c.

Probability that non red balls, that is $\{GG,GY,YG,YY\}$ is as shown below.

p(non red balls)=(3/13*2/12)+(3/13*3/12)+(3/13*3/12)+(3/13*2/12)

=6/156+9/156*9/156+6/156

=30/156

=5/26

d.

Probability that both balls are green $\{GG\}$ is,

p(both balls are green)=(3/13*2/12)=6/156=1/26