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Question

A five-question quiz is taken in which the first and second questions have four answer choices, the third and fourth questions have three answer choices, and the last question has five answer choices. If a student randomly marks an answer for each question, what is the expected number of questions he will answer correctly?

A

$0.27$

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B

$0.96$

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C

$1$

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D

$1.37$

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Solution

The correct option is D $1.37$Explanation for the correct option:First and second questions have four answer choices, the third and fourth questions have three answer choices, and the last question has five answer choicesAssuming that only one option is correct for each question, then the probabilities for choosing the correct options for the questions is:$P\left(Q1\right)=\frac{1}{4}\phantom{\rule{0ex}{0ex}}P\left(Q2\right)=\frac{1}{4}\phantom{\rule{0ex}{0ex}}P\left(Q3\right)=\frac{1}{3}\phantom{\rule{0ex}{0ex}}P\left(Q4\right)=\frac{1}{3}\phantom{\rule{0ex}{0ex}}P\left(Q5\right)=\frac{1}{5}$If a student randomly marks an answer for each question, the expected number of questions he will answer correctly will be$=\frac{1}{4}+\frac{1}{4}+\frac{1}{3}+\frac{1}{3}+\frac{1}{5}=\frac{1}{2}+\frac{2}{3}+\frac{1}{5}=1.37$Hence, option $\left(D\right)$ is the correct answer.

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