A factory manufactures watches and 100 watches are packed in a box. The probability that a watch is defective is given by 0.004. Find the probability that there are less than 3 defective watches in a box.
answer:
We need to find the probability that there are either 0, 1 or 2 defective watches in the box. Since the probability that a watch is defective is 0.004, the probability that a watch is not defective is 1 - 0.004 = 0.996, and thus the desired probability is
(0.004^0*(0.996)^100 + (100 C 1)(0.004)^1(0.996)^99 + (100 C 2)(0.004)^2(0.996)^98
= (0.996)^100 + 100*(0.004)(0.996)^99 + 4950(0.004)^2*(0.996)^98 = 0.992245
to 6 decimal places, or about 99.2%.
is it correct ?
