Statistics / Unit 6: Probability
6.1 Sample Spaces and Basic Probability
Notes
The probability of an event is a number from 0 to 1 that tells how likely it is. The sample space is the list of all possible outcomes.
- If all outcomes are equally likely, $\displaystyle P(A) = \frac{\text{number of outcomes in } A}{\text{number of outcomes in the sample space}}$.
- $P = 0$ means impossible and $P = 1$ means certain. A probability can never be below 0 or above 1.
- Probability describes the long-run relative frequency (the law of large numbers). Past results do not change the chance of the next independent trial.
- Example: Two coins give the sample space HH, HT, TH, TT, so $\displaystyle P(\text{exactly one head}) = \frac{2}{4} = \frac{1}{2}$.
Practice
Two fair coins are flipped. What is the probability of exactly one head?
The sample space is HH, HT, TH, TT, and two of the four outcomes have exactly one head.
A fair six-sided die is rolled. What is the probability of rolling a prime number?
The primes are 2, 3 and 5, so $\displaystyle \frac{3}{6} = \frac{1}{2}$.
A fair coin has landed heads 5 times in a row. What is the probability of heads on the next flip?
Coin flips are independent, so past flips do not change the next one.
Ready for more? Take the Unit 6 test.