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Question
A coin is tossed three times. Find P (A/B) in each of the following:
A = Heads on third toss, B = Heads on first two tosses.
Solution
Consider the given events.
A = Heads on third toss
B = Heads on first two tosses
Clearly,
A = {(H, H, H), (H, T, H), (T, H, H), (T, T, H)}
B = {(H, H, H), (H, H, T)
\[\text{ Now } , \]
\[A \cap B = \left\{ H, H, H \right\}\]
\[ \therefore \text{ Required probability} = P\left( A/B \right) = \frac{n\left( A \cap B \right)}{n\left( B \right)} = \frac{1}{2}\]
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