Question

Refer to Question 74 above. The probability that exactly two of the three balls were red, the first ball being red, is ______.

विकल्प

• `1/3`

• `4/7`

• `15/28`

• `5/28`

Answer 1

Refer to Question 74 above. The probability that exactly two of the three balls were red, the first ball being red, is `4/7`.

Explanation:

Let E₁ be the event that first ball is red.

E₂ be the event that exactly two of the three balls are red.

∴ P(E₁) = P(R) . P(R) . P(B) + P(R) . P(R) . P(R) + P(R) . P(B) . P(R) + P(R) . P(B) . P(B)

= `5/8*4/7*3/6 + 5/8*4/7*3/6 + 5/8*3/7*4/6 + 5/8*3/7*2/6`

= `60/336 + 60/336 + 60/336 + 30/336`

= `210/336`

P(E₁ ∩ E₂) = P(R) . P(B) . P(R) + P(R) . P(R) . P(B)

= `5/8*3/7*4/6 + 5/8*4/7*3/6`

= `60/336 + 60/336`

= `120/336`

∴ `"P"("E"_2/"E"_1) = ("P"("E"_1 ∩ "E"_2))/("P"("E"_1))`

= `(120/336)/(210/336)`

= `4/7`