Question
Five defective bulbs are accidentally mixed with twenty good ones. It is not possible to just look at a bulb and tell whether or not a bulb is defective. Four bulbs are drawn at random from this lot. Find the mean number of defective bulbs drawn.
Solution
Let us denote by X, the number of defective bulbs. Clearly X can take the values 0, 1, 2, 3, 4.
P(X = 0) = (no defective bulb) = P(all 4 goods ones)
P(X = 1) = P(1 defective and 3 good ones)
P(X = 2) = P(2 defective and 2 good ones)
P(X = 3) = P(3 defective and one good one)
P(X = 4) = P(all 4 defective)
∴ Probability distribution table is
P(X = 0) = (no defective bulb) = P(all 4 goods ones)
P(X = 1) = P(1 defective and 3 good ones)
P(X = 2) = P(2 defective and 2 good ones)
P(X = 3) = P(3 defective and one good one)
P(X = 4) = P(all 4 defective)
∴ Probability distribution table is
