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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 45
Total: 101
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 ?
Solution:  
Let E1 : ‘1, 2, 3 or 4 is shown on die’ i.e., she tosses a coin once.
⇒P(E1)=
4
6
=
2
3
 and P(E2)=
2
6
=
1
3
Let A : ‘exactly one head shows up’, then P(A|E1) = P (head shows up when coin is tossed once) =
1
2
 and P(A|E2) = P (exactly one head shows up when coin is tossed thrice) =
3
8

Hence, the required probability,
=P(E1|A)=
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)
=
1
2
×
2
3
(
1
2
×
2
3
)+(
3
8
×
1
3
)
=
8
11
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