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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.

Respuesta :

premedchemist
We can break this down:
The student has a one out of five chance of getting a correct answer, and a four out of five chance of an incorrect answer. We can express the students odds of getting one incorrect answer as 4/5. In order to get the odds of two wrong answers, we need to multiply this answer again by the odds of choosing a wrong answer. Therefore:
The odds of one wrong answer = 4/5
The odds of two wrong answers = (4/5) * (4/5) = 16/25 chance of getting both of the questions wrong.

Using it's concept, it is found that the probability that she answered neither of the problems correctly is given by:

[tex]p = \frac{16}{25}[/tex]

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, for each question, there are 5 options, 4 of which are wrong, hence, the probability of getting both wrong is:

[tex]p = \frac{4}{5} \times \frac{4}{5} = \frac{16}{25}[/tex]

More can be learned about the probability concept at https://brainly.com/question/15536019

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