Expected value of a two-coin win-two lose-seven game

Question

You toss two fair coins together once. Exactly one head pays you $2, two heads costs you $7, and no heads pays nothing. What is your expected profit?

Short answer

$-\text{\char36}0.75$ . The four outcomes are equally likely and pay $0$ , $2$ , $2$ and $-7$ , so the mean is $\tfrac{0+2+2-7}{4}=-\tfrac34$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited
Sample Spaces, Events, and the Probability Axioms

Start with a free lesson: Expectation, Variance and Covariance is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free