Question

In the Hawaiian Beach Boy surf board vendor scenario, what if the fine was increased to $190 but the probability of a fine decreased to one in 20 days, 5%? What would be the expected value – Exp(RS) -- of continuing to rent surfboards? Assume the other numbers stay the same. He makes $300/day and to rent boards from friends costs him $100 a day. So, he makes $200 a day. Write out the expected value formula, plug in the numbers, and show the math. Hint: the Exp(RS) should be higher than the previously calculated $160.

Answer 1

$190.50

Explanation:

Expected value is the sum of each possible income multiplied by its probability.

There's a 5% chance that the vendor makes $200 and loses $190 (net gain of $10).

There's a 95% chance that the vendor makes $200 and loses $0 (net gain of $200).

So the expected value is:

Exp(RS) = $10 × 0.05 + $200 × 0.95

Exp(RS) = $190.50