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Question
Solution
The repeated guessing of correct answers from multiple-choice questions is Bernoulli trials. Let X represent the number of correct answers by guessing in the set of 5 multiple-choice questions.
Probability of getting a correct answer is, p `= 1/3`
` ∴ "q" = 1 - "p" = 1 - 1/3 = 2/3`
Clearly, X has a binomial distribution with n = 5 and p `= 1/3`
∴ p (X = x) = `""^"n""C"_"x" "q"^("n"-"x")"p"^"x"`
` = ""^5"C"_"x" (2/3)^(5-"x").(1/3)^"x"`
P (guessing more than 4 correct answers) = P(X ≥ 4)
= P (X = 4)+ (X = 5)
` = ""^5"C"_4(2/3).(1/3)^4 + ""^5"C"_5(1/3)^5`
` = 5. 2/3 . 1/81 + 1 . 1/243`
` = 10/243 + 1/243`
` = 11/243`
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