Question

When taking a 14-question multiple-choice test, where each question has 5 possible answers, it would be unusual to get __ or more questions correct by guessing alone.

A) 2
B) 3
C) 4
D) 5

Answer 1

The probability of getting 5 or more questions correct by guessing alone on a 14-question multiple-choice test is 0.0933.

Step-by-step explanation:

When taking a 14-question multiple-choice test, where each question has 5 possible answers, it would be unusual to get 5 or more questions correct by guessing alone.

To calculate the probability of getting 5 or more questions correct, we need to calculate the probability of getting 0, 1, 2, 3, and 4 questions correct by guesswork and subtract that from 1 (the total probability).

The probability of guessing a question correctly is 1/5, so the probability of guessing a question incorrectly is 4/5. Using the binomial probability formula, we can calculate the probabilities:

1. Probability of guessing 0 correct answers: (4/5)^14 = 0.0432
2. Probability of guessing 1 correct answer: C(14, 1) * (1/5)^1 * (4/5)^13 = 0.1200
3. Probability of guessing 2 correct answers: C(14, 2) * (1/5)^2 * (4/5)^12 = 0.2243
4. Probability of guessing 3 correct answers: C(14, 3) * (1/5)^3 * (4/5)^11 = 0.2890
5. Probability of guessing 4 correct answers: C(14, 4) * (1/5)^4 * (4/5)^10 = 0.2302

Total probability of guessing 0, 1, 2, 3, or 4 questions correctly: 0.0432 + 0.1200 + 0.2243 + 0.2890 + 0.2302 = 0.9067

Subtracting this from 1, we get the probability of getting 5 or more questions correct by guessing alone: 1 - 0.9067 = 0.0933

Therefore, it would be unusual to get 5 or more questions correct by guessing alone on a 14-question multiple-choice test.