Question

Erin is taking a multiple choice test with 4 answer choices where she earns 5 points for every correct answer, loses 2 points for every incorrect answer and 0 points for leaving a question blank. If she doesn't know the answer to a question, what should she do?

A) Erin should guess the answer since the expected value is 1/4 so she is more likely to gain points than lose them.
B) Erin should guess the answer as she could earn 5 points if she gets it right and she has 1/4 chance of getting it right.
C) Erin should leave the question blank since the expected value is -1/4 so she is more likely to lose points than gain them.
D) Erin should leave the question blank since the expected value is 1/4 and most teachers won't give partial points on a test.

Answer 1

Erin should leave the question blank because the expected value of guessing is -0.25, indicating that she would be statistically more likely to lose points than gain them.

Step-by-step explanation:

When Erin is taking a multiple choice test with 4 answer choices, and she earns 5 points for a correct answer, loses 2 points for an incorrect answer, and gets 0 points for an unanswered question, she needs to consider the expected value to determine her best strategy.

Let's calculate the expected value (EV) for Erin if she guesses an answer:

1. Probability of getting the answer right: 1/4
2. Points gained if she gets it right: 5 points
3. Probability of getting the answer wrong: 3/4 (since there are 4 options in total)
4. Points lost if she gets it wrong: -2 points

Using this information:

EV = (1/4 * 5) + (3/4 * -2) = 1.25 - 1.5 = -0.25

Since the expected value is negative (-0.25), Erin is statistically more likely to lose points by guessing. Therefore, Option C is correct: Erin should leave the question blank since the expected value is -1/4 so she is more likely to lose points than gain them.