Answer

Solution

1. 1

   $P(A) = P(C) = P(D) = 1/2$, $P(G) = 1/4$.

2. 2

   \begin{itemize}[leftmargin=*]

3. 3
   • $A\cap G = \{HH\}$, $P = 1/4$. $P(A)P(G) = 1/8 \ne 1/4$. Not independent.
4. 4
   • $A\cap D = \{HH\}$, $P = 1/4$. $P(A)P(D) = 1/4$. Independent.
5. 5
   • $C\cap D = \{HH\}$, $P = 1/4$. $P(C)P(D) = 1/4$. Independent.
6. 6
   • $A\cap C = \{HH\}$, $P = 1/4 = P(A)P(C)$. Independent.
7. 7

   \end{itemize}

8. 8

   Hence the FALSE statement is (B): $A$ and $G$ are not independent (the question asks for the false claim).

Answer structure / marking notes

Content note