Question

From a sealed box containing a dozen apples it was found that 3 apples are perished. Obtain the probability distribution of the number of perished apples when 2 apples are drawn at random. Also find the mean and variance of this distribution.

Answer 1

Step-by-step explanation:

You have 3 cases to consider which make up your distribution: 0, 1 and 2 perished apples are drawn.

So all you need to do is compute the probability for each case.

Drawing no perished apple is the probablitiy of drawing a good apple from 12 with 9 being good ones and then drawing a good one from 11 with 8 remaining good ones. That makes: 9/12 * 8/11 ~= 0.55

Similarily the probablitiy of drawing two perished apples is: 3/12 * 2/11 ~= 0.05

The last case is then just the remaining probability: 1 – 0.55 – 0.05 = 0.4