On a multiple-choice exam with three possible answers for each of the five questions, what is the probability that a student would get fouror more correct answers just by guessing?

Answer: 11/243

Step-by-step explanation:

Each question has 3 options: 2 incorrect and 1 correct

Probability P (correct guessing) = 1/3

P (wrong guessing) = 2/3

Probability P (4 answers correct) = 5C4 * (1/3) ^4 * (2/3) ^1

Probability P (5 answers guessed correctly) = 5C5 * (1/3) 5

Therefore Probability P (4 or more answers correct) = P (4) + P (5) = (10/3^5) + (1/3^5)

P (4 or more correct answers) = 11/243