There are 1000 components in a box of which 10 are known to be
defective. two components are selected at random. What is the
probability that
a)both are defective
Probability that the first one is defective = 10/1000 = 1/100.
Probability that the second one is defective, given that the first
was defective is is 9/999 = 1/111.
P(both are defective) = (10/1000)(9/999) = (1/100)(1/111) = 1/11100
b)neither is defective
There are 990 non-defective ones.
Probability that the first one is not defective = 990/1000 = 99/100.
Probability that the second one is not defective, given that the
first was not defective is is 989/999.
P(neither is defective) = (99/100)(989/999) = 10879/11100
c)just one is defective
Probability that the first one is defective is 10/1000 or 1/100
Probability that the second one is not defective given that
the first was defective is 990/999 = 110/111
That's (1/100)(110/111) = 11/1110
Probability that the first one is not defective is 990/1000 or
99/100
Probability that the second one is defective given that the
first was not defective is 10/999
That's also = 11/1110
The probability that one or the other will occur is the sum of
those two probabilities:
11/1110 + 11/1110 = 11/555
Edwin
