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

a student ran out of time on a multiple - choice exam and randomly guessed the answers for two problems. each problem had 4 answer choices - a, b, c, d - and only one correct answer. what is the probability that he answered both 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 4 answer choices - a, b, c, d - and only one correct answer. what is the probability that he answered both of the problems correctly? write your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate probability of one - problem correct

The probability of getting one multiple - choice problem correct by guessing is $\frac{1}{4}$ since there is 1 correct answer out of 4 choices.

Step2: Use multiplication rule for independent events

Since the two problems are independent events, the probability of getting both correct is the product of the probabilities of getting each one correct. So the probability is $\frac{1}{4}\times\frac{1}{4}$.

Step3: Simplify the product

$\frac{1}{4}\times\frac{1}{4}=\frac{1\times1}{4\times4}=\frac{1}{16}$.

Answer:

$\frac{1}{16}$