Final answer:
To find the probability of getting 3 or fewer questions correct on a 32-question multiple choice exam, where each question has three possible choices, we can use the binomial distribution. The probability of getting a question correct by random guessing is 1/3, and the probability of getting a question wrong is 2/3. We can calculate the probability of getting 0, 1, 2, or 3 questions correct using the binomial distribution equation.
Step-by-step explanation:
To find the probability of getting 3 or fewer questions correct, we need to determine the probability of getting 0, 1, 2, or 3 questions correct. The student randomly guesses each answer on a 32-question multiple choice exam, where each question has three possible choices. The probability of getting a question correct by random guessing is 1/3, and the probability of getting a question wrong is 2/3.
Since the student did not study and is guessing randomly, we can use the binomial distribution to calculate the probability.
- For getting 0 questions correct: P(X=0) = C(32,0) * (1/3)^0 * (2/3)^(32-0)
- For getting 1 question correct: P(X=1) = C(32,1) * (1/3)^1 * (2/3)^(32-1)
- For getting 2 questions correct: P(X=2) = C(32,2) * (1/3)^2 * (2/3)^(32-2)
- For getting 3 questions correct: P(X=3) = C(32,3) * (1/3)^3 * (2/3)^(32-3)
The probability of getting 3 or fewer questions correct is the sum of these probabilities: P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3).