13 Balls are in an urn. 4 are blue, 3 are black, 6 are red. If...

13 Balls are in an urn. 4 are blue, 3 are black, 6 are red.

If two balls are taken out of the urn at the same time, what is the probability that the balls are of different color? What is the probability that the balls would be different colors if you took one ball and put it back before drawing the second?

Expert Solution

a) Total balls = 4 + 3 + 6 = 13

P(both balls are same) = P(both are blue) + P(both are black) + P(both are red)

= 4C2/13C2 + 3C2/13C2 + 6C2/13C2

= 6/78 + 3/78 + 15/78

= 24/78

= 4/13

P(both would be of different colors) = 1 - P(both will be of same colors) = 1 - 4/13 = 9/13 = 0.6923

b) P(both will be of same colors) = P(both are blue) + P(both are black) + P(both are red)

= (4/13)² + (3/13)² + (6/13)²

= 61/169

P(both would be of different colors) = 1 - P(both will be of same colors) = 1 - 61/169 = 0.6391

orchestra answered 11 months ago

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