A charity is choosing between two fundraising phone scripts. The charity wants the higher expected net donation per call over many calls. (Net donation = donation received minus the cost of the call.)
Strategy A: Each call costs $1. With probability 0.15, the person donates $20; with probability 0.85, the person donates $0.
Strategy B: Each call costs $2. With probability 0.10, the person donates $35; with probability 0.90, the person donates $0.
Which strategy has the greater expected value of net donation over many repetitions?
- Strategy A, because a donation is more likely (0.15 vs 0.10).
- Strategy B, because it has the larger possible donation ($35).
- Strategy A, because it has the greater expected net donation over many calls. (correct answer)
- Strategy B, because its expected value is $0.10(35) - 2 = .
Explanation: The skill here is comparing strategies using expected value, which helps determine the better choice for long-term average outcomes. Expected value is calculated as the long-run average net donation per call, found by multiplying each possible net donation by its probability and summing them up. For Strategy A, the expected value is computed by weighting the net donations of $20 - $1 and $0 - $1 by their probabilities of 0.15 and 0.85, resulting in $2. For Strategy B, weighting $35 - $2 and $0 - $2 by 0.10 and 0.90 gives $1.50. Since Strategy A has the higher expected value, it yields better average net donation over many calls, though individual results may vary. A tempting distractor is selecting Strategy B for its larger possible donation of $35, disregarding the costs and probabilities. To apply this, always multiply outcomes by their probabilities and sum for each strategy, then compare the totals rather than isolated high or low values.