12.3: An Introduction to Probability

1. 12.3: An Introduction to Probability

2. The probability indicates the likelihood that an event will occur. It is given by a number between 0 and 1. P=0.5 P=0 P=1 The event will occur The event is equally likely to occur or not occur The event will not occur You will roll an even number on a fair six-sided die. You will roll a number between 1 and 6 on a fair six-sided die You will roll an 8 on a fair six-sided die. There are two types of probability: theoretical and experimental.

3. Theoretical Probability When all outcomes are equally likely, the theoretical probability is given by Example: You roll a fair six-sided die, numbered 1 to 6. Find the probability of • Rolling a 5 • Rolling a multiple of 3 • Rolling an 8

4. Example: you roll a fair six-sided die, numbered 1 to 6. find the probability of • Rolling a 5 • Rolling a multiple of 3 c) Rolling an 8 =0.333 = 33.3% =0.0=0%

5. Experimental Probability A probability based on data is given by Example: Yesterday the vet saw 3 Chihuahuas, 5 Labradors, 4 poodles, and 3 beagles. Find the experimental probability that a randomly selected owner has each breed of dog.

6. Experimental Probability Example: 15 dogs 3 Chihuahuas 5 Labradors 4 poodles 3 beagles. =0.2 = 20% =0.333 = 33.3% 0.267 = 26.7% =0.2 = 20%

7. Geometric Probability Another type of theoretical probability is the geometric probability. This is found by comparing the ratio of 2 measurements. Example: You spin the spinner shown. What is the probability of each outcome?

8. Example: Lose a turn Receive 10 Move 2 Free turn Lose 5

9. Vocabulary Outcome – the result of a single trial of an experiment. There are 3600 in a circle.