Question

A multiple-choice test consists of 8 questions. Each question has answer choices of a, b, c, d, and e, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that she gets more than 1 of them correct?Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

Answer 1

The probability that she gets more than one of them correct is equal to:

`1-P,`

where P is the probability that she has exactly one correct or zero answers correct.

Now, the probability that she has exactly one correct or zero answers correct is equal to the probability that she has exactly one answer correct plus the probability that she has all the answers incorrect.

The probability that she has all answers incorrect is:

`(4)/(5)*(4)/(5)*(4)/(5)*(4)/(5)*(4)/(5)*(4)/(5)*(4)/(5)*(4)/(5)\text{.}`

Simplifying the above multiplication we get:

`((4)/(5))^8.`

Now, the probability that she gets at most one answer correct is:

`(8!)/(1!(8-1)!)*((4)/(5))^7((1)/(5))^{}.`

Therefore,

`\begin{gathered} P=((4)/(5))^8+(8!)/(1!(8-1)!)*((4)/(5))^7((1)/(5))^{} \\ =0.1678+0.3355=0.5033. \end{gathered}`

Finally, the probability that she gets more than 1 of them correct is:

`1-0.5033=0.4967.`

Answer:

`0.50`