Question

A multiple-choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly?

Answer 1

The probability of a student guessing all questions correctly on a 5-question multiple-choice test with 5 possible answers each is 1/3125 or 0.032%.

Step-by-step explanation:

The probability of guessing all questions correctly on a multiple-choice test with 5 questions and 5 possible answers is the product of the probabilities of choosing each answer correctly. Since the student has a 1 in 5 chance of getting a question right, the probability for one question is 1/5 or 0.20. To find the probability of getting all 5 questions correct, we multiply the individual probabilities:

P(choosing all five numbers correctly) = P(choosing 1st number correctly) × P(choosing 2nd number correctly) × ... × P(choosing 5th number correctly)

Therefore, this works out to:
(1/5) × (1/5) × (1/5) × (1/5) × (1/5) = (1/5)^5 = 1/3125

The probability is 1/3125, which is equivalent to 0.00032 or 0.032%.

Answer 2

The probability of guessing all questions correctly on a 5-question multiple-choice test with 5 possible answers per question is (1/5)^5, which is 1/3125, or a 0.032% chance.

Step-by-step explanation:

The subject of the question is Mathematics, as it involves calculating probability, which is a mathematical concept. Specifically, it's a question often encountered at the high school level. To calculate the probability of guessing all questions correctly on a multiple-choice test with 5 questions each having 5 possible answers, you need to consider the probability of getting one question right and then raise that to the number of questions since they are independent events.

The probability of guessing one question right is 1 out of 5, or 1/5. Since there are 5 independent questions, you multiply the probability of getting one question right by itself five times (1/5 × 1/5 × 1/5 × 1/5 × 1/5), which is the same as (1/5)^5. The probability of guessing all five correct is therefore (1/5)^5, which equals 1/3125, or 0.00032. That's a 0.032% chance of guessing all answers correctly.