mdlemuslopez
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On a quiz there are four multiple-choice questions worth 3 points each and two true/false questions worth 1 point each. Each multiple-choice question has five possible choices. If a student randomly guesses on each question, what is the expected value of the student's score on the test?

Respuesta :

Answer: Expected value would be [tex]\dfrac{17}{5}[/tex]

Step-by-step explanation:

Since we have given that

Number of multiple choice question = 4

Number of true false questions = 2

Number of points for each multiple choice question = 3

Number of points for each true false question = 1

Number of choices in multiple choice = 5

Probability of getting correct answer in multiple choice question = [tex]\dfrac{1}{5}[/tex]

Probability of getting correct answer in true false question = [tex]\dfrac{1}{2}[/tex]

Expected value of the student's score on the test would be

[tex]E(x)=\sum xp(x)\\\\E(x)=4\times 3\times \dfrac{1}{5}+2\times 1\times \dfrac{1}{2}\\\\E(x)=\dfrac{12}{5}+1\\\\E(x)=\dfrac{12+5}{5}=\dfrac{17}{5}[/tex]

Hence, expected value would be [tex]\dfrac{17}{5}[/tex]

aksnkj

The performance of a student in the quiz is estimated. The expected score of the student in the quiz will be 3.4 points.

Given information:

The number of multiple-choice questions is 4. The points rewarded for each MCQ are 3 points.

The number of true/false questions is 4. The points rewarded for each T/F are 3 points.

Each MCQ has 5 options and there are 2 possibilities for each T/F question.

So, the probability of answering an MCQ correctly is,

[tex]P=\dfrac{1}{5}[/tex]

The probability of answering a T/F correctly is,

[tex]P=\dfrac{1}{2}[/tex]

The expected value of a student's score can be calculated as,

[tex]E(x)=\sum xp(x)\\E(x)=4\times3\times\dfrac{1}{5}+2\times1\times\dfrac {1}{2}\\E(x)=\dfrac{12}{5}+1\\E(x)=\dfrac{17}{5}=3.4[/tex]

Therefore, the expected score of the student in the quiz will be 3.4 points.

For more details, refer to the link:

https://brainly.com/question/23857268

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