The Probability Question
The Probability Question asks for the likelihood of each outcome given an option, and combined with utilities, it yields the expected value to guide decision-making.
THE IDEA
The Probability Question
So our jelly bean analysis must take account of the probabilities of picking a red, yellow, or green bean. We do that in the fifth step by asking the Probability Question: If this option is selected, what is the probability of this outcome? Applied to the first option-outcome combination (bet red, get red), the Probability Question reads as follows: If I bet on picking a red bean, what is the probability of my picking a red bean? There are 90 beans: 45 red, 36 yellow, and 9 green. Therefore, the probability of picking a single red bean is .5, a yellow .4, and a green .1. We enter these probabilities into the tree (Figure 14-5). Note that the probabilities for the outcomes of a single option must equal 1.0.
We have established the utilities of the three options ($2, $3, and $4) and their respective probabilities (.5, .4, and .1). How can we now use these calculations to guide our decision as to which wager best serves our self-interest? We compare wagers by calculating expected value.
When to use it
Evaluating investment opportunities with uncertain returns.
Choosing between medical treatments with different success rates and side effects.
Deciding on a marketing strategy with varying probabilities of success.
Comparing job offers with different salary, bonus, and growth prospects.
FROM THEORY TO EVERYDAY LIFE
In practice
Jelly Bean Bet
In a jar of 90 jelly beans (45 red, 36 yellow, 9 green), the probability of picking red is 0.5, yellow is 0.4, green is 0.1. Prizes are $2 for red, $3 for yellow, $4 for green. If a draw instead paid the listed prize for whichever color appeared, its expected payout would be 0.5*$2 + 0.4*$3 + 0.1*$4 = $2.6. That is a different payoff rule from betting on one color; valuing that bet also requires the payout for a losing outcome.
A MOMENT TO REFLECT
Put it to work.
How would you estimate probabilities for outcomes when they are not explicitly given?
What insights does expected value provide when comparing multiple risky options?
How might the framing of probabilities (e.g., percentages vs. frequencies) influence your decision?
CONTINUE THE CONVERSATION
Source texts
- The Thinkers Toolkit by Morgan D Jones