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CBSE Class 12 Math 2018 Solved Paper

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Question : 22
Total: 29
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 s or 6 with the die?
Solution:  
Let E1 be the event that the outcome on the die is 1 or 2
P (E1) =
2
6
 =
1
3
let E2 be the event that the outcome on the die is 3,4,5 or 6
P (E2) =
4
6
 =
2
3
let A be the event that exactly one tail comes
So
P (
A
E1
) =
2
8
 (A occurs given that E1 had already occured, coin tossed thrice)
P (
P
E2
) =
1
2
 (A occures given that E2 had already occured, coin tossed once
By Bayes's theorem, (A had already occured, probability that E2 had occured)
P (
E2
A
) =
P(E2)×P(
A
E2
)
P(E2)×P(
A
E2
)+P(E1)×P(
A
E1
)

=
2
3
×
1
2
2
3
×
1
2
+
1
3
×
3
8
=
8
11
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