Chapter 14.2, Problem 4E

Let $E$ and $F$ be events in a sample space $S$.

(a) The probability of $E$ and $F$ occurring is $P\left(E\cap F\right)=$______________.

(b) If the occurrence of $E$ does not affect the probability of the occurrence $F$, then the events are called ____________. So in tossing a coin twice, the event $E$, “getting heads on the first toss,” and the event $F$, “getting heads on the second toss,” are ____________.

(c) If $E$ and $F$ are independent events, then the probability of $E$ and $F$ is $P\left(E\cap F\right)=$________.