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Question : 13
Total: 29
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?
Solution:
Let X denote the number of questions answered correctly by guessing in multiple choice examinations.
Probability of getting a correct answer by guessing, p =
Therefore, q, the probability of an incorrect answer by guessing is = 1 -
P (X = x) =
C x . q n − x . p x
C x . (
) 5 − x . (
) x
P (guessing more than 4 correct answers) = P (X ≥ 4)
= P (X = 4) + P (X = 5)
=
C 4. (
) 5 − 4 . (
) 4
C 5. (
) 5 − 5 . (
) 5
= 5 ×(
) . (
) (
)
C r
=
Probability of getting a correct answer by guessing, p =
Therefore, q, the probability of an incorrect answer by guessing is = 1 -
P (X = x) =
P (guessing more than 4 correct answers) = P (X ≥ 4)
= P (X = 4) + P (X = 5)
=
= 5 ×
=
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