Question

17. A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that three washers are selected at random, without replacement, from the lot.

(a) What is the probability that all three washers are thicker than the target?

(b) What is the probability that the third washer selected is thicker than the target if the first two washers selected are thinner than the target?

(c) What is the probability that the third washer selected is thicker than the target?

Answer 1

a) Probability all 3 are thicker = 30/50 * 29/49 * 28/48 = 29/140

b) if first two were thinner than probability of 3rd one thicker is 30/(50-2) = 30/48 = 5/8

c) Probability third is thicker = P(only 3rd is thicker) + P(1st and 3rd are thicker) + P(2nd and 3rd are thicker) + P(all are thicker)

= 30*20*19/48*49*50 + (30*29)*20/(50*49*48) + (30*29)*20/(50*49*48) + 30/50 * 29/49 * 28/48

= 3/5