(a) Denote the to equal 1 if the ith pick is from member A, and 0 otherwise. then we're interested in . If you then note that the are (5,.3) binomial random variables, you compute
(b)We're now interested in:
where I is the condition that all samples consist of union workers from A or B.
Again this can be solved using the binomial probability distribution, but with an adjusted probability of success equal to: 3/10*10/9=1/3. Using this, we get
P.S. by the way,