Question

On a multiple-choice test, each question has 4 possible answers. A student does not know the answers to three questions, so the student guesses. What is the probability that the student gets all three questions wrong? The probability that the student gets all three questions wrong is . What is the probability that the student gets all three questions right? The probability that the student gets all three questions right is .

Answer 1

P(making 3 wrong guesses) = 27/64

P(making 3 right guesses) = 1/64

Explanation:

Number of possible answers per question = 4

Number of right answer per question = 1

Number of wrong answers per question = (4 - 1) = 3

Probability = (Number of required outcomes / Number of Total possible outcomes)

A.) probability of guess 3 questions wrong :

Probability of making a wrong guess = (number of wrong options / total number of options

P(making a wrong guess) = 3/4

Therefore,

P(making 3 wrong guesses) = 3/4 × 3/4 × 3/4 = (27/64)

B.) probability of making 3 right guesses:

P(making a right guess) = (number of right options per question / total number of options per question)

P(making a right guess) = 1/4

P(making 3 right guesses) =(1/4 × 1/4 × 1/4) = 1/64