Question

A batch of 40 injection-molded parts contains 6 parts that have suffered excessive shrinkage (a) If two parts are selected at random, and without replacement, what is the probability 6. that the second part selected is one with excessive shrinkage? (b) If three parts are selected at random, and without replacement, what is the probability that the third part selected is one with excessive shrinkage? 7. If two events under study , event A and even B. What would be a proof that A is independent of B?

Answer 1

6;

(a)

Out of 60, 6 parts are with excessive shrinkage and 60-6 = 54 are good. After selecting the first good item we have 59 items remaining out of which 6 are good. So the probability that second part selected is one with excessive shrinkage and first is good will be

p = (54/60) * (6/59) = 0.0915

(b)

The probability that third part selected is one with excessive shrinkage and first two are good will be

p = (54/60) *(53/59) * (6/58) = 0.0836

7:

If P(A and B) =P(A)P(B) then events A and B will be independent.