Practice Events (Formal) in Math

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

Quick Recap

A formal event is a subset of the sample space — a collection of outcomes to which a probability is assigned; events can be simple (one outcome) or compound (many outcomes).

An event is a question like 'Did I roll higher than 3?' that has yes/no answer.

Example 1

easy
Rolling a fair die: Event A = rolling an even number. Find P(A) and P(A^c), and verify the complement rule.

Example 2

medium
At least one approach: Find P(\text{at least one head in 3 coin flips}) using the complement rule.

Example 3

easy
If P(\text{rain tomorrow}) = 0.35, find P(\text{no rain tomorrow}) and explain the complement rule.

Example 4

hard
A system has 3 independent components, each failing with probability 0.1. The system fails if at least one component fails. Find P(\text{system fails}) using the complement rule.
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