Final answer:
The probability of getting exactly 2 questions correct on a 10-question multiple choice quiz is 0.2816; at most 2 questions correct is 0.5256; and at least 2 questions correct is 0.9214.
Step-by-step explanation:
The probability of guessing multiple-choice questions on a quiz involves binomial probability. Here, the student guesses on a 10-question multiple-choice quiz with 4 options per question.
A. You get exactly 2 questions correct.
The probability of getting exactly 2 questions correct is calculated by a combination of choosing 2 out of 10 questions times the probability of getting 2 questions right and 8 questions wrong.
Probability = (10 choose 2)*(1/4)^2*(3/4)^8 = 0.2816
B. You get at most 2 questions correct.
This requires the sum of probabilities of getting 0, 1, or 2 questions correct.
Probability = (10 choose 0)*(1/4)^0*(3/4)^10 + (10 choose 1)*(1/4)^1*(3/4)^9 + (10 choose 2)*(1/4)^2*(3/4)^8 = 0.5256
C. You get at least 2 questions correct.
This is 1 minus the probability of getting 0 or 1 question correct.
Probability = 1 - [(10 choose 0)*(1/4)^0*(3/4)^10 + (10 choose 1)*(1/4)^1*(3/4)^9] = 0.9214