Question

Two fair coins $S_1$ and $S_2$ are tossed independently once. Let the events $E, F,$ and $G$ be defined as follows:
$E$: Head appears on $S_1$
$F$: Head appears on $S_2$
$G$: The same outcome (head or tail) appears on both $S_1$ and $S_2$
Then which of the following statements is NOT correct?

• A. $E$ and $F$ are independent
• B. $F$ and $G$ are independent
• C. $E$ and $G^C$ are independent
• D. $E, F,$ and $G$ are mutually independent

Answer 1

Answer: (D)

$E, F,$ and $G$ are mutually independent

Answer 2

The correct option is (D): $E, F,$ and $G$ are mutually independent