Question

Two urns contain the set of balls as given in the following table. 

Title	White	Red	Black
Urn 1	10	6	9
Urn 2	3	7	15

One ball is drawn from each urn and find the probability that 

(i) both balls are red, 

(ii) both balls are of the same colour.

Answer 1

(i) Let A be the event of drawing a red from urn 1, 

P(A) = \(\frac{6}{25}\)

Let B be the event of selecting a red ball in urn 2. 

P(B) = \(\frac{7}{25}\)

∴ P(both balls are red) = P(A).P(B) [∵ the events are independent] 

= \(\frac{6}{25}\) x \(\frac{7}{25}\)

= \(\frac{42}{625}\)

Let W₁, R₁, B₁ represents white, red, and black balls drawn from urn 1 and W₂, R₂, B₂ represents white, red, and black balls from urn 2. 

(ii) P(both balls are of the same colour) = P(W₁W₂) + P(R₁R₂) + P(B₁B₂) [∵ Events are mutually exclusive] 

= P(W₁) P(W₂) + P(R₁) P(R₂) + P(B₁) P(B₂) [∵ Events are independent]