Example 7 - If coin shows head, toss it again but if shows tail - Examples

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Example 7 Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 4’ given that ‘there is at least one tail’. A coin is tossed. if the coin shows head, it is tossed again. If it shows tail, then a die is thrown. Hence different value of probabilities are We need to find the probability that the die shows a number greater than 4, given that there is at least one tail. Now, F : Number greater than 4 on the die E : at least one tail We need to find P(E|F) Also, E ∩ F = {(T, 5), (T, 6)} So, P(E ∩ F) = P(T, 5) + P(T, 6) So, P(E ∩ F) = P(T, 5) + P(T, 6) = 1﷮12﷯ + 1﷮12﷯ = 2﷮12﷯ = 1﷮6﷯ Now, P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 1﷮6﷯﷮ 3﷮4﷯﷯ = 1﷮6﷯ × 4﷮3﷯ = 𝟐﷮𝟗﷯ Therefore, required probability is 2﷮9﷯

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