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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. B and C .
Solution
\[S = \left[ \left( H H H \right) \left( H H T \right) \left( H T H \right) \left( H T T \right) \left( T H H \right) \left( T H T \right) \left( T T H \right) \left( T T T \right) \right]\]
\[\left( ii \right) P\left( C \right) = \frac{2}{8} = \frac{1}{4}\]
\[P\left( B \right) = \frac{4}{8} = \frac{1}{2}\]
\[P\left( B \cap C \right) = \frac{2}{8} = \frac{1}{4} \neq P\left( B \right)P\left( C \right)\]
\[\text{ Thus, B and C are not independent events } .\]
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