The probability that a bulb produced by a factory will fuse after 150 days of use is `0.05`. If a sample of such 5 bulbs are taken out, then match the probabilities in column I with their respective values in column II and choose the correct option from the codes given below.

Options

A. `{:(A,B,C,D),(2,4,1,3):}`
B. `{:(A,B,C,D),(4,3,2,1):}`
C. `{:(A,B,C,D),(4,3,1,2):}`
D. `{:(A,B,C,D),(4,1,3,2):}`

Answer

B

Explanation

Let X represents the number of bulbs that will fuse after 150 days of use in an experiment of 5 trials . The trials are Bernoulli trials .
X has a binomial distribution with n=5
`p=0.05 and q=0.95`
`P(X=r) =""^(5)C_(r).(0.05)^(r)(0.95)^(5-r)`
A. Required probability
`P(X=0)=""^(5)C_(0)p^(0)q^(5)=(0.95)^(5)`
B. Required probability
`=P(X le 1) =P(0) + P(1) = ""^(5)C_(0)p^(0)q^(5)+""^(5)C_(1)p^(1)q^(4)`
`=q^(5)+5pq^(4)=q^(4)(q+5p)=(0.95)^(4)[0.95+5xx(0.05)]`
`=(0.95)^(4)[0.95 +0.25]=(0.95)^(4)xx1.2`
C. Required probability
`=P(X gt 1)=1-{P(0) + P(1)}`
`=1-(0.95)^(4)xx1.2`
D. Required probability
=P (atleast one) `=P(X ge1)`
`=1-P(0)=1-(0.95)^(5)`