Answer
a)0.04
b)0.2
c)0.000000512
Work Step by Step
a) Events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the date of hire of one doesn't affect the other, hence here $P(B|A)=P(B)$. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{1}{5}\cdot\frac{1}{5}=0.04.$
b) Say one person was hired on a day, then the other has 5 days in the week to be hired on, form which 1 is the same as the other's, hence the probability of the person being hired on the same day is, $\frac{1}{5}=0.2.$
c) By using the result and methodology from part b), the probability is:$(\frac{1}{5})^9=0.000000512.$
