Question

what is the expected number of black balls among n ::; b w d balls drawn at random from a box containing b black balls, w white balls, and d balls drawn at random from another box of bo black balls and wo white balls? assume all draws are made without replacement.

Answer 1

To find the expected number of black balls among n balls drawn at random from the given boxes, calculate the probability of drawing a black ball at each step and then multiply them together.

Step-by-step explanation:

To find the expected number of black balls among n balls drawn at random from the given boxes, we need to calculate the probability of drawing a black ball at each step. Let P(B1) be the probability of drawing a black ball from the first box, P(B2) be the probability of drawing a black ball from the second box, and P(B3) be the probability of drawing a black ball from the second box after drawing a black ball from the first box.

The expected number of black balls can be calculated as:

E = n x P(B1) x P(B2) x P(B3)