On a multiple choice test you guess he answers to two questions. Each question has five choices.
What is the probability that you both answers correct?
To find the probability of guessing both answers correctly, we need to first calculate the probability of guessing one question correctly, and then multiply that by the probability of guessing the second question correctly.
The probability of guessing one question correctly is 1 out of 5, since there are 5 choices and you can only choose one. Therefore, the probability of guessing one question correctly is 1/5.
Since the two questions are independent events (the outcome of one question does not affect the outcome of the other question), we can multiply the probabilities together to find the probability of both events occurring. Thus,
Probability of guessing both questions correctly = Probability of guessing first question correctly * Probability of guessing second question correctly
= 1/5 * 1/5
= 1/25
So, the probability that you guess both questions correctly is 1/25.