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

1. both balls are red
2. both balls are of the same colour.

Answer 1

i. Let A be the event of drawing a red from urn 1

P(A) = `6/25`

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

P(B) = `7/25`

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

= `6/25 xx 7/25`

= `42/625`

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

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]

= `10/25 xx 3/25 + 6/25 xx 7/25 + 9/25 xx 15/25`

= `1/625 [30 + 42 + 135]`

= `207/625`