Question

4. Urn A contains 3 red and 3 black balls, whereas urn B contains 4 red and 6 black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be the same color?

Answer 1

Urn	Red	Black	Total
A	3	3	6
B	4	6	10

Urn A :

Prob of Red in Urn A , P(RA) = 3/6

Prob of Black in Urn A , P(BA) = 3/6

Urn B :

Prob of Red in Urn B , P(RB) = 4/10

Prob of Black in Urn B , P(BB) = 6/10

Now, one ball is taken from each urn. Both of them have to be of same color. There are two cases here:

1. Both the balls are Red :

Probability that both the balls are Red , P(R)= P(RA)* P(RB) = 3/6 * 4/10 = 12/60

2. Both the balls are Black :

Probability that both the balls are Black, P(B) = P(BA)* P(BB) = 3/6 * 6/10 = 18/60

Therefore, Total probability = Probability that both of them are either Black or Red, P(R $\tiny \bigcup$ B) = P(R) + P(B) ( Since these two are independent events).

Therefore, Total probability = 12/60 + 18/60 = 30/60 = 1/2.

Hope I clarified your query.