Learn / Library / Expected value

Today or tomorrow

Expected valueEasy

Today's offer is $2$ , $4$ or $6$ dollars, each equally likely. If you decline it, tomorrow you must take the result of a fair $6$ -sided die roll in dollars. You choose to maximise your expected payout. What is it?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Tomorrow's average is the benchmark for today's offer.

Solution

Tomorrow's roll is worth $\frac{7}{2}$ on average.
Decline today's offer only when it is below $\frac{7}{2}$ , which happens for $2$ ; accept $4$ and $6$ .
The expected payout is $\frac{\frac{7}{2} + 4 + 6}{3} = \frac{9}{2}$ .

Answer: $\frac{9}{2}$

Next question Back to the library