Question

A urn contains 7 white 3 black ball. Two ball are drawn random. Compute the expected number of white ball

Answer 1

Answer:

The expected number of white balls is 1.4

Hope this helps.

Step-by-step explanation:

Let X be the number of white balls.  We want to calculate E(X).

P(X=0) = P(0 white balls)

 = (# ways of choosing 2 black balls) / (# ways of choosing 2 balls)

 = ( 3 × 2 / 2 )  /  ( 10 × 9 / 2 )

 = 3 / 45

 = 1 / 15

P(X=1) = P(1 white ball)

 = (# ways of choosing 1 white and 1 black) / (# ways of choosing 2 balls)

 = ( 3 × 7 ) / ( 10 × 9 / 2 )

 = 21 / 45

 = 7 / 15

P(X=2) = P(2 white balls)

 = (# ways of choosing 2 white balls) / (# ways of choosing 2 balls)

 = ( 7 × 6 / 2 ) / ( 10 × 9 / 2 )

 = 21 / 45

 = 7 / 15

Now for the expected value:

E(X) = 0 × P(X=0)  +  1 × P(X=1)  +  2 × P(X=2)

    = 0  +  7 / 15  +  2 × 7 / 15

    = 3 × 7 / 15

    = 7 / 5

    = 1.4