CBSE Class 12 Math 2012 Solved Paper

© examsnet.com
Question : 13
Total: 29
How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?
Solution:  
Let the man toss the coin n times. The n tosses are n Bernoulli trials
Probability (p) of getting a head at the toss of a coin is
1
2

⇒ p =
1
2
⇒ q =
1
2

∴ P (X = x) =
n
Cxpnxqx
=
n
Cx(
1
2
)
nx
(
1
2
)
x
=
n
Cx(
1
2
)
n

It is given that
P getting at least one head) >
80
100

⇒ P (X ≥ 1) > 0.8
⇒ 1 - P (X = 0) > 0.8
⇒ 1 -
n
Cn
1
2n
> 0.8
n
C0
1
2n
< 0.2
1
2n
< 0.2
2n >
1
0.2
= 5
2n > 5 ... (1)
The minimum value of n which satisfies the given inequality is 3.
Thus, the man should toss the coin 3 or more than 3 times.
© examsnet.com
Go to Question: