A box contains 10 red , 3 blue, and 7 white balls , two balls are drawn at random from the box on after the other without replacement. What is the probability that both balls are of the same colour

P(XX) = 69/190

Step-by-step explanation:

Given:

20 balls, 10R, 3B, 7W.

Two taken without replacement.

Find probability of two identical colours.

P(XX)

Solution:

We use the multiplication rule for the probability of each of the 2 draws

P(RR) = 10/20*9/19 = 90/380

P(BB) = 3/20*2/19 = 6/380

P(WW) = 7/20*6/19 = 42/380

Probability of drawing two identical coloured balls

P(XX) = (90+6+42)/380 = 138/380 = 69/190

answer: 45