A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices a, b, c, d, e and only one correct answer. What is the probability that she answered neither of the problems correctly?
Do not round your answer.
4/5 is chance wrong
problems are independent so
(4/5)(4/5) = 16/25
To find the probability that the student answered neither of the problems correctly, we need to determine the probability that the student guessed incorrectly for both problems.
Since each problem has 5 answer choices, the student has a 1 in 5 chance of guessing the correct answer for each problem. Therefore, she has a 4 in 5 chance of guessing incorrectly for each problem.
To calculate the probability of both events happening (guessing incorrectly for the first problem and guessing incorrectly for the second problem), we multiply the probabilities together.
The probability that she guessed incorrectly for the first problem is 4/5, and the probability that she guessed incorrectly for the second problem is also 4/5.
So, the probability that she answered neither of the problems correctly is (4/5) * (4/5).
Multiplying these fractions gives us 16/25.
Therefore, the probability that the student answered neither of the problems correctly is 16/25.
To find the probability that the student answered neither of the problems correctly, we first need to find the probability that she answered each problem correctly.
Since each problem has 5 answer choices, and only one of them is correct, the probability of answering a problem correctly by random guessing is 1/5.
Therefore, the probability of not answering a problem correctly by random guessing is 1 - 1/5 = 4/5.
Since the student guesses randomly on each problem independently, we can multiply the probabilities together to find the combined probability:
P(neither problem is answered correctly) = P(problem 1 is not answered correctly) * P(problem 2 is not answered correctly)
= 4/5 * 4/5
= 16/25
Therefore, the probability that the student answered neither of the problems correctly is 16/25.