Question

A multiple-choice test consists of 10 questions. Each question has answer choices of a,b,c,d, and e, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that she gets more than 2 of them correct? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

Answer 1

To find the probability that the student guesses more than 2 questions correctly, we need to calculate the probabilities of getting 0, 1, or 2 correct and subtract that from 1. The probability is approximately 0.32 or 32%.

Step-by-step explanation:

To find the probability that the student guesses more than 2 questions correctly, we need to find the probability of getting 0, 1, or 2 questions correct and subtract that from 1 (total probability). Let's calculate it step by step:

1. Probability of getting 0 questions correct: (4/5)^10
2. Probability of getting 1 question correct: C(10, 1) * (1/5) * (4/5)^9
3. Probability of getting 2 questions correct: C(10, 2) * (1/5)^2 * (4/5)^8
4. Total probability: 1 - the probability of getting 0, 1, or 2 questions correct

Now, let's calculate the probabilities and round the final answer to two decimal places.

P(0 questions correct) = (4/5)^10 = 0.1074

P(1 question correct) = C(10, 1) * (1/5) * (4/5)^9 = 0.2686

P(2 questions correct) = C(10, 2) * (1/5)^2 * (4/5)^8 = 0.3020

Total probability = 1 - (P(0) + P(1) + P(2)) = 1 - (0.1074 + 0.2686 + 0.3020) = 0.3219

Therefore, the probability that the student gets more than 2 questions correct is approximately 0.32 or 32%.