# A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, both the balls are of the same color? - Mathematics and Statistics

Sum

A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, both the balls are of the same color?

#### Solution

Let Y1 ≡ the event that yellow ball is drawn from first bag

B1 ≡ the event that brown ball is drawn from first bag

Y2 ≡ the event that yellow ball is drawn from second bag

B2 ≡ the event that brown ball is drawn from second bag

∴ P(Y1) = 3/8, P(B1) = 5/8

P(Y2) = 4/10, P(B2) = 6/10

Let A = event that both balls are of same colour i.e., both are yellow or both are brown.

∴ A = (Y1 ∩ Y2) ∪ (B1 ∩ B2)

Since events in the brackets are mutually exclusive

∴ P(A) = P(Y1 ∩ Y2) + P(B1 ∩ B2)

= P(Y1)·P(Y2) + P(B1)·P(B2)   ...[events are independent]

= 3/8*4/10 + 5/8*6/10

= 42/80

= 21/40.

Concept: Independent Events
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