NCERT Class XII Mathematics Chapter - - Solutions
© examsnet.com
Question : 77
Total: 101
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is
a) at least once
(b) exactly once
(c) at least twice ?
a) at least once
(b) exactly once
(c) at least twice ?
Solution:
Let p be the probability of success that is chance of winning a prize =
⇒ q = 1 − p = 1 −
=
and let X has a binomial distribution withn = 50 , p =
, q =
∴ P ( X = r ) = n C r ( q ) n − r p r
(a) P (the probability of person wins a prize at least once) = P(X ≥ 1)
= 1 − P ( X = 0 )
= 1 − 50 C 0 q 50 p 0
= 1 − (
) 50
(b) P (the probability of person winning a prize exactly once) = P(X = 1)
= 50 C 1 q 49 p 1
= 50 (
) 49 (
)
=
(
) 49
(c) P (the probability of person wins a prize at least twice) = P(X ≥ 2)
= 1 – (P(0) + P(1)) = 1 –( 50 C 0 q 50 p 0 + 50 C 1 q 49 p 1 )
= 1 − ( ( 1 ) q 50 ( 1 ) + 50 q 49 p )
= 1 − q 49 ( q + 50 p )
= 1 − (
) 49 [
+ 50 ×
]
= 1 − (
) (
) 49
and let X has a binomial distribution with
(a) P (the probability of person wins a prize at least once) = P(X ≥ 1)
(b) P (the probability of person winning a prize exactly once) = P(X = 1)
(c) P (the probability of person wins a prize at least twice) = P(X ≥ 2)
= 1 – (P(0) + P(1)) = 1 –
© examsnet.com
Go to Question: