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CBSE Class 12 Math 2012 Solved Paper

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Question : 28
Total: 29
A girl throws a die. If she get 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 two times and notes the number of heads obtained. If she obtained exactly two heads, what is the probability that she threw 1, 2, 3 OR 4 with the die?
Solution:  
Consider the following events:
E1 = Getting 5 OR 6 in a single throw of the die
E2 = Getting 1, 2, 3 OR 4 in a single throw of the die
A = Getting exactly 2 heads
We have to find, P(E2/A).
Since P (E2/A) =
P(A|E2)P(E2)
P(A|E1)P(E1)+P(A|E2)P(E2)

Now, P(E1) =
2
6
 =
1
3
 and P(E2) =
4
6
 =
2
3
Also,
P (A|E1) = Probability of getting exactly 2 heads when a coin is tossed 3 times =
3
8
And, P (A|E2) = Probability of getting 2 heads when a coin is tossed 2 times =
1
2
∴ P (E2|A) =
1
2
×
2
3
3
8
×
1
3
+
1
2
×
2
3
 =
1
3
1
3
(
3
8
+1)
 =
1
3
1
3
(
8+3
8
)
 =
8
11
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