Answer
a) $\frac{1}{365}$
b)$\frac{1}{133,225}.$
c)$\frac{1}{365}$
Work Step by Step
a) There are 365 days in a year, hence the probability of the person being born on July 4 is, $\frac{1}{365}.$
b) Events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the birthday of someone doesn't affect the other, hence here $P(B|A)=P(B)$. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{1}{365}\cdot\frac{1}{365}=\frac{1}{133,225}.$
c) Say one person was born on a day, then the other has 365 days in a year, hence the probability of the person being born on the same day (just like in part a)) is, $\frac{1}{365}.$
