Question

Urn I contains two red chips and four white chips: urn II, three red and one white. A chip is drawn at random from urn I and transferred to urn II. Then a chip is drawn from urn II. What is the probability that the chip drawn from urn II is red?

Answer 1

Urn I -> 2 R and 4 W
Urn II -> 3 R and 1 W

There are two possibilities
1. Chip drawn from Urn I is red
2. Chip drawn from Urn II is white

1. Chip drawn from Urn I is red
Probability that a chip drawn from urn II is red if a chip drawn from Urn I is red,
P1 = 2/6 * 4/5
2/6 indicates selecting a red chip from Urn I and 4/5 indicates selecting a red chip from Urn II. There would be 4 red chips in Urn II when 1 red chip from Urn I is transferred to Urn II

2. Chip drawn from Urn II is white
P2 = 4/6 * 3/5

Hence required probability, P = P1 + P2
P = 2/6 * 4/5 + 4/6 * 3/5
P = 0.666666667