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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 76
Total: 101
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answer just by guessing ?
Solution:  
Let p be the probability of success that the answer is correct =
1
3
If p=
1
3
,q=1−
1
3
=
2
3
∴ X has a binomial distribution with n=5,p=
1
3
,q=
2
3
∴P(X=r)=nCr(q)n−rpr
∴ Required probability = P(four or more correct answers)
= P(X ≥ 4) = P(X = 4) + P(X = 5)
=5C4(
2
3
)1(
1
3
)4+5C5(
2
3
)0(
1
3
)5
=
11
243
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