Question

Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?

विकल्प

• `7/15`

• `8/15`

• `4/19`

• `8/19`

Answer 1

`8/15`

Explanation:

Let E₁, E₂ and A be the events defined as follows:

E₁ = Red ball is transferred from bag P to bag Q

E₂ = Blue ball is transferred from bag P to bag Q

A = The ball drawn from bag Q is blue

As the bag P contains 6 red and 4 blue balls,

P(E₁) = `6/10 = 3/5` and P(E₂) = `4/10 = 2/5`

Note that E₁ and E₂ are mutually exclusive and exhaustive events.

When E₁ has occurred i.e., a red ball has already been transferred from bag P to Q, then bag Q will contain 6 red and 6 blue balls, So, P(A|E₁) = `6/12 = 1/2`

When E₂ has occurred i.e., a blue ball has already been transferred from bag P to Q, then bag Q will contain 5 red and 7 blue balls, So, P(A|E₂) = `7/12`

By using law of total probability, we get

P(A) = P(E₁) P(A|E₁) + P(E₂) P(A|E₂)

= `3/5 xx 1/2 + 2/5 xx 7/12`

= `8/15`