Questions: Standardized Test: You are trying to answer a multiple-choice question on a standardized test. There are five choices. If you get the question right, you gain one point, and if you get it wrong, you lose 1/3 point. Assume you can eliminate one of the five choices, and you choose one of the remaining four at random as your answer. What is the expected value of the number of points you get? Round the answer to four decimal places. The expected value of the number of points you get is .

Standardized Test: You are trying to answer a multiple-choice question on a standardized test. There are five choices. If you get the question right, you gain one point, and if you get it wrong, you lose 1/3 point. Assume you can eliminate one of the five choices, and you choose one of the remaining four at random as your answer.

What is the expected value of the number of points you get? Round the answer to four decimal places.

The expected value of the number of points you get is .

Transcript text: Standardized Test: You are trying to answer a multiple-choice question on a standardized test. There are five choices. If you get the question right, you gain one point, and if you get it wrong, you lose $\frac{1}{3}$ point. Assume you can eliminate one of the five choices, and you choose one of the remaining four at random as your answer. What is the expected value of the number of points you get? Round the answer to four decimal places. The expected value of the number of points you get is $\square$ .

Solution

Solution Steps

Step 1: Calculate the Probability of Selecting the Correct Answer

The probability of selecting the correct answer is calculated as the inverse of the remaining choices after elimination, which is $\frac{1}{n-m}$. Given $n=5$ choices and $m=1$ eliminations, the probability is $\frac{1}{5-1} = 0.25$.

Step 2: Calculate the Probability of Selecting an Incorrect Answer

The probability of selecting an incorrect answer is calculated by subtracting the probability of a correct answer from 1, which is $\frac{n-m-1}{n-m}$. With $n=5$ choices and $m=1$ eliminations, the probability is $\frac{3}{4} = 0.75$.

Step 3: Calculate the Expected Value