Products produced by a machine has a 3% defective rate. (a) what is the probability that the first defective occurs in the fifth item inspected? (b) what is the probability that the first defective occurs in the first five inspections? (c) what is the expected number of inspections before the first defective occurs?

Step-by-step explanation:

Given that the Products produced by a machine has a 3% defective rate.

Each product is independent of the other with a constant prob of being defective as 0.03

X - no of defects is binomial with p =0.03

a)  the probability that the first defective occurs in the fifth item inspected

=Prob for first 4 non defective and 5th defective

=

(b) the probability that the first defective occurs in the first five inspections

=P(X=1) in binomial with n=5

= 0.9915

c) the expected number of inspections before the first defective occurs

Expected defects in n trials = np

Expected number of inspection before the first defect = 1/p

= 33.33

=34

(c) What is the expected number of inspections before the first defective occurs?

goog may have it for you

-1/2 +2

step-by-step explanation: