Q2. Assume that in a particular neighborhood, 10 percent of the households own no bicycle, 25
percent own one bicycle, 40 percent own two bicycles, and 25 percent own three bicycles. Suppose
each bicycle is equally likely (and independently) to be either black or white. If a household is
selected at random from this neighborhood,
(a) What is the joint probability mass function of the number of black bicycles and the number of
white bicycles in this household?
(b) Given that the selected household has at least one black bicycle, compute the conditional
probability mass function of the number of white bicycles in the household