NCERT Class XII Mathematics Chapter - - Solutions
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Question : 72
Total: 101
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one will fuse after 150 days of use.
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one will fuse after 150 days of use.
Solution:
We have p = 0.05 =
=
q = 1 −
=
X has a binomial distribution withn = 5 , p =
, q =
∴ P ( X = r ) = n C r q n − r p r
(i)P ( X ) = 5 C 0 q 5 p 0 = 1 × (
) 5 × 1 = ( 0.95 ) 5
(ii) P(X = 0) + P(X = 1)= n C 0 q n p 0 + n C 1 q n − 1 p
= ( 1 × q 5 × 1 ) + 5 C 1 q 4 p
= (
) 5 + 5 (
) 4 (
)
= (
) 4 (
) = ( 1.2 ) ( 0.95 ) 4
(iii) P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 1 - (P(X = 0)+ P(X = 1))
= 1 −
(
) 4 = 1 − ( 1.2 ) ( 0.95 ) 4
(iv) P(X = 1) + P(X = 2) +...........+ P(X = 5)
= 1 − P ( X = 0 ) = 1 − (
) 5 = 1 − ( 0.95 ) 5
X has a binomial distribution with
(i)
(ii) P(X = 0) + P(X = 1)
(iii) P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 1 - (P(X = 0)+ P(X = 1))
(iv) P(X = 1) + P(X = 2) +...........+ P(X = 5)
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