Find the probability of correctly answering the first 5 questions on a multiple choice test if random guesses are made and each question has 4 possible answers

Question

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Answer 1

Since each question has 4 possible answers, the probability of selecting the right answer for an individual question is 1 in 4, which is  0.25.  To do this 5 times in a row, assume the individual probabilities are independent, in which case the probability of selecting the right answer 5 times in a row is the product of the individual probabilities of selecting the correct answer once.  This becomes

 

P = 0.25 x 0.25 X ... x 0.25 = (0.25)⁵ = 9.766 x 10^-4