Ex 13.3, 10

Transcript

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) = 𝑃 𝐴﷯ . 𝑃(𝐶|𝐴)﷮𝑃 𝐴﷯ . 𝑃 𝐶|𝐴﷯ + 𝑃 𝐵﷯ . 𝑃 𝐶|𝐵﷯﷯ 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﷯﷯ = 𝟖﷮𝟏𝟏﷯ Therefore, required probability is 8﷮11﷯