A multiple choice question has 4 options. What is probability that a student choosing answers at random gets fewer than 3 answers out of 10 right.
Each multiple choice question has four options of which one is the correct answer. The probability that a student making a guess and choosing answers at random gets any one of them right is 1/4. On the other hand the probability that a wrong answer is chosen is 1 - 1/4 = 3/4.
The probability of the student getting less than 3 answers right is required. This implies either 0 or 1 or 2 answers are correct. The probability that none of the answers are right is (3/4)^10. The probability that only 1 answer is right is 10*(1/4)*(3/4)^9 and the probability that only 2 of them are right is 45*(1/4)^2*(3/4)^8. Adding the three gives 0.5255
The probability that the student gets less than 3 answers right if they are chosen at random is approximately equal to 0.5255.