Question

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 he answered both of the problems correctly?

do not round your answer. (if necessary, consult a list of formulas.)

Explanation:

Identify the probability of a single event

Using the Probability of Events knowledge point

$$ P(\text{Correct}) = \frac{1}{5} = 0.2 $$

Calculate the joint probability

Using the Independent Events Probability knowledge point

$$ P(\text{Both Correct}) = P(\text{Correct}) \times P(\text{Correct}) = 0.2 \times 0.2 = 0.04 $$

Answer:

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 he answered both of the problems correctly?

Do not round your answer.

<blank>0.04</blank>