Lesson 15 of 1524
Probability
A probability is a number from 0 to 1. The complement is whatever is left.
Practice this chapterIf outcomes are equally likely, the probability is the count of favorable outcomes divided by the count of all outcomes. The complement rule says P(not A) = 1 − P(A).
Independent events do not change each other’s chances, so you multiply. Expected value is the sum of each payoff times its probability.
Expected value
E = Σ (value × probability)
Weight each outcome by how likely it is, then add.
Worked example
A game pays $4 with probability 1/4 and pays $0 otherwise. What is the expected value?
- 1The other outcome has probability 1 − 1/4 = 3/4, and its payoff is $0.
- 2Expected value adds payoff × probability for every outcome: E = 4 × (1/4) + 0 × (3/4).
- 34 × (1/4) = 1, and 0 × (3/4) = 0.
- 4E = 1 + 0 = 1.
Result: $1
Why. You do not get $4 on every play. One play in four pays $4 and the rest pay nothing, so the long-run average per play is $1. The zero payoff still belongs in the sum, and it contributes 0.
Mutually exclusive means they cannot happen together. Independent means one does not change the other. Those are different ideas.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.