A multiple-choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly?

Solution:

Given the probability of guessing the first question correctly = 1/5

Let P be the probability of guessing 5 questions correctly.

The probability of getting a correct guess is 1/5 and it is the same for every question.

P(getting first question correct) = 1/5

P(getting the first two questions correct)

= 1/5 × 1/5 = (1/5)²

P(getting the first 3 questions correct) =(1/5)³

P(getting the first 4 questions correct)= (1/5)⁴

P(getting all questions correct)= (1/5)⁵

P(getting all questions correct) = (1/5)⁵ = (1/3125)

A multiple-choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly?

Summary:

A multiple-choice test has 5 questions each with 5 possible answers, the probability of guessing all the questions correctly is 1/3125.