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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.
Check the independence of A and B.
Solution
\[S = \left[ \left( H H H \right) \left( H H T \right) \left( H T H \right) \left( H T T \right) \left( T H H \right) \left( T H T \right) \left( T T H \right) \left( T T T \right) \right]\]
\[\left( i \right) P\left( A \right) = \frac{4}{8} = \frac{1}{2}\]
\[P\left( B \right) = \frac{4}{8} = \frac{1}{2}\]
\[P\left( A \cap B \right) = \frac{2}{8} = \frac{1}{4} = P\left( A \right)P\left( B \right)\]
\[\text{ Thus, A and B are independent events } .\]
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