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The probability of guessing any one is 1 out of 4, or 0.25.

Assume that the choices are made independently. Then, if X is the random variable which represents the number of successes (correct guesses), X is a Binomial variable with n = 5 and p = 0.25.

Then Prob(X = 3) = 5C3*p^3*(1-p)^(n-3)

= 10*(0.25)^3*(0.75)^2

= 0.088, approx.

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