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# Suppose a Girl Throws a Die. If She Gets 1 Or 2 She Tosses a Coin Three Times and Notes the Number of Tails. If She Gets 3,4,5 Or 6, She Tosses a Coin Once and Notes Whether a ‘Head’ - CBSE (Science) Class 12 - Mathematics

#### Question

Suppose a girl throws a die. If she gets 1 or 2 she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3,4,5 or 6 with the die ?

#### Solution

Let E1 be the event that the outcome on the die is 1 or 2 and E2 be the event that the outcome on the die is 3, 4, 5 or 6. Then,

P(E_1) = 2/6 = 1/3 and P(E_2)  = 4/6 = 2/3

Let A be the event of getting exactly one 'tail'.

P(A|E1) = Probability of getting exactly one tail by tossing the coin three times if she gets 1 or 2 = 3/8

P(A|E2) = Probability of getting exactly one tail in a single throw of a coin if she gets 3, 4, 5 or 6 = 1/2

As, the probability that the girl threw 3, 4, 5 or 6 with the die, if she obtained exactly one tail, is given by P(E2|A).

So, by using Baye's theorem, we get

P(E_2|A) = (P(E_2)xxP(A|E_2))/(P(E_1)xxP(A|E_1)+P(E_2) xx P(A|E_2))

= (2/3 xx 1/2)/((1/3xx3/8+2/3xx1/2))

= (2/6)/((1/8","+","1/3))

= ((2/6))/((11/24))

= (24xx2)/(11xx6)

= 8/11

So, the probability that she threw 3, 4, 5 or 6 with the die if she obtained exactly one tail is 8/11

Is there an error in this question or solution?
Solution Suppose a Girl Throws a Die. If She Gets 1 Or 2 She Tosses a Coin Three Times and Notes the Number of Tails. If She Gets 3,4,5 Or 6, She Tosses a Coin Once and Notes Whether a ‘Head’ Concept: Baye'S Theorem.
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