Integrated Math 2 / Unit 9: Probability
9.1 Sample Spaces and Basic Probability
Notes
A sample space is the set of all possible outcomes. An event is a subset of those outcomes.
- For equally likely outcomes: $\displaystyle P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$.
- Probabilities range from 0 (impossible) to 1 (certain).
- The complement of an event has probability $1 - P(\text{event})$.
- Example: tossing two coins has 4 outcomes (HH, HT, TH, TT), so $\displaystyle P(\text{two heads}) = \frac{1}{4}$.
Practice
Two coins are tossed. What is the probability of getting two heads?
The sample space is HH, HT, TH, TT, and only HH is favorable.
A fair six-sided die is rolled. What is the probability of rolling a prime number?
The primes on a die are 2, 3 and 5, so $\displaystyle \frac{3}{6} = \frac{1}{2}$. The number 1 is not prime.
The chance of rain tomorrow is $35\%$. What is the chance it does not rain?
The complement is $100\% - 35\% = 65\%$.
Ready for more? Take the Unit 9 test.