Practice Probability as Expectation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Probability can be interpreted as the long-run relative frequency of an event over infinitely many identical trials of a random experiment.

P(\text{heads}) = 0.5 means if you flip many times, about half will be heads.

Example 1

easy
A basketball player makes free throws with probability 0.75. In 200 free throws, how many do we expect her to make?

Example 2

medium
A game has three outcomes: win \10 (prob 0.2), break even \0 (prob 0.5), lose \$5 (prob 0.3). Calculate the expected value and interpret what it means for 1000 games.

Example 3

easy
A school expects 15% of students to be absent on any given day. If there are 300 students, how many absences are expected?

Example 4

hard
An insurance company charges \200/year for a policy. It pays \10,000 if the insured event occurs (probability 0.01) and \$0 otherwise. Calculate the insurance company's expected profit per policy.
← Back to Probability as Expectation Worked Examples Formula Explained