Question

A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5 questions if you guess randomly on each question?A. 0.9936B. 0.2C. 0.0264D. 0.0003

Answer 1

If there are 10 questions with 5 answer choices, then first we need to find out the probability of getting the first questions randomly correct.

Therefore, that is:

`\begin{gathered} Probability\text{ of getting 1 answer correct= }(1)/(5) \\ \\ Then\text{ if we need to get the second question correct it is:} \\ (1)/(5)(first\text{ question\rparen x }(1)/(5)=\text{ \lparen}(1)/(5))^2 \\ \\ And\text{ for the other questions applies the same. Therefore, if we need 5 correct answers, then:} \\ (1)/(5)\text{ x }(1)/(5)x\frac{1}{5\frac{}{}}x(1)/(5)x\text{ }(1)/(5)=\text{ \lparen}(1)/(5))^5\text{ = }(1)/(3125)=\text{ 0.0003} \end{gathered}`

The answer is D. 0.0003