a student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. each…

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? write your answer as a fraction in simplest form.

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? write your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate probability of getting one question wrong

The probability of getting a single - multiple - choice question wrong is $\frac{4}{5}$ since there are 5 choices and 4 incorrect ones.

Step2: Use the multiplication rule for independent events

Since the two guesses are independent events, the probability of getting both questions wrong is the product of the probabilities of getting each question wrong. So the probability $P=\frac{4}{5}\times\frac{4}{5}=\frac{16}{25}$.

Answer:

$\frac{16}{25}$