Question

A box contains
22
​red,
22
white and
33
green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same​ color?

Answer 1

Red = 22

White = 22

Green = 33

Total = 77

Case 1:

Both are Red

Probability of selecting 2 balls from 77 balls =

Probability of selecting 2 Red from 22 Red =

So,

P(2 Red) = 231/2926 = 0.0789

Case 2:

Both are White

Probability of selecting 2 balls from 77 balls =

Probability of selecting 2 White from 22 White =

So,

P(2 White) = 231/2926 = 0.0789

Case 3:

Both are Green

Probability of selecting 2 balls from 77 balls =

Probability of selecting 2 Green from 33 Green =

So,

P(2 Green) = 528/2926 = 0.1805

So,

P(same color) = 0.0789 + 0.0789 + 0.1805 = 0.3383

So,

Answer is:

0.3383