Question

A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row. C and A

Answer 1

\[S = \left[ \left( H H H \right) \left( H H T \right) \left( H T H \right) \left( H T T \right) \left( T H H \right) \left( T H T \right) \left( T T H \right) \left( T T T \right) \right]\]

\[ P\left( C \right) = \frac{1}{4}\]
\[P\left( A \right) = \frac{1}{2} \]
\[P\left( C \cap A \right) = \frac{1}{8} = P\left( C \right)P\left( A \right)\]
\[\text{ Thus, A and C are independent events.} \]