CLASS 9 · LEARNING KNOWLEDGE
Probability and expected value
How it works
The expected value is the sum of possible values weighted by their probabilities. It describes a long-term average, not a guaranteed single outcome. In money games, distinguish between payout and profit relative to the stake.
Note
E(X) = Σ xᵢ·P(X = xᵢ); P(complement event) = 1 − P(event).
E(X) = Σ xᵢ·P(X = xᵢ); P(complement event) = 1 − P(event).
An example
A lottery box contains 7 winning tickets and 3 blanks. What is P(no win) in percent? Round to two decimal places. Give the result in %.
P(Lose) = 1 − P(Win) = 1 − 7 / 10 = 3 / 10. Result: 30 %.
Try it yourself now
50 Exercises · three difficulty levels · selection and number input
To the learning unit →Own explanation and own practice exercises by AmyMath. Subject reference framework: KMK Educational Standards Mathematics ESA/MSA. The topic assignment may vary by federal state.