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On a multiple choice examination with th...

On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

A

`(3)/(243)`

B

`(1)/(243)`

C

`(25)/(243)`

D

`(11)/(243)`

Text Solution

Verified by Experts

The correct Answer is:
D
(D) Let X donotes the number of correct answers given by the candidate. It is a case of Bernoulli trials with n=5, choice question with 3 options.
`:." " p=(1)/(3) " and " q=1-p=1(1)/(3)=(2)/(3)`
Clearly, X has a binomial distribution with n=5.
`p=(1)/(3) " and " q=(2)/(3)`.
`P(X=r)=""^(5)C_(r )((1)/(3))^(r ).((2)/(3))^(5-r)`
Required probability =P (four or more correct answers)
`=P(X ge 4)=P(4)+P(5)=""^(5)C_(4)p^(4)q+""^(5)C_(5)p^(5)q^(0)`
`=""^(5)C_(4)((1)/(3))^(4)((@)/(3))^(1)+""^(5)C_(5)((1)/(3))^(5).((2)/(3))^(0)`
`=5xx(2)/(3)xx(1)/(3^(4))+(1)/(3^(5))=(11)/(3^(5))=(11)/(243)`
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