In the US, it is reported that 72% of woman have some type of piercing. The most popular piercing location is the ear. A recent study reported the following statistics on the popularity of alternative piercings (percent of the total non-ear piercings). The categories are disjoint.
Navel: 33%
Nose: 19%
Tongue: 9.5%
Eyebrow: 8%
Lip: 4%
Other: 26.5 %
a) What is the probability that of 10 women selected at random, 3 have a nose piercing, 2 have their tongue pierced, and 4 have a navel piercing?
b) What is the probability that of 10 women selected at random, at least 2 have a tongue piercing?
c) What is the distribution for the sample space X if X is the # of women who select an eyebrow piercing?