Ex 13.3, 10 - Suppose a girl throws die. If she gets a 5 or 6 - Bayes theorem

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Ex 13.3, 10 Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die? Let A : 1, 2, 3, 4 appear on the die B : 5, 6 appear on the die C : exactly one head is obtained We need to find the Probability that if exactly one head is obtained on the toss of a coin, she threw 1, 2, 3 or 4 with the die i.e. P(A|C) P(A|C) = . ( | ) . | + . | Putting values in formula, P(A|C) = 2 3 1 2 2 3 1 2 + 1 3 3 8 = 2 3 1 2 2 1 3 1 2 [2 + 3 4 ] = 2 2 + 3 4 = 2 11 4 = Therefore, required probability is 8 11

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