Probability topic

Question

A bag contains 3 white ,4 black and 5 green . when two balls are drawn from it random , then which of the following could not be the Probability that they are of different color

 

(a)13/66

(b)32/66

(c)47/66

(d)35/36

Answer 1

There's only one probability that the balls are a different color:

 

P(White then Different Color) = (3/12)(9/11) = 27/132

P(Black then Different Color) = (4/12)(8/11) = 32/132

P(Green then Different Color) = (5/12)(7/11) = 35/132

 

That's a total probability of 27/132 + 32/132 + 35/132 = 94/132 = 47/66

 

So, (c) is the only correct probability. The probabilities that could not be the probability that they are different colors are (a), (b), and (d).