1. MTH 232 Section 14.1 The Basics of Probability

2. Overview Probability is the mathematics of uncertainty, in which the likelihood that a chance event occurs is measured by a number between 0 (no chance of occurring) and 1 (must certainly occur). Students in grades 3 – 5 should begin to learn about this measurement. Previous to this, students will have begun to describe events as certain, likely, or impossible. Students should explore probability through experiments that have only a few outcomes (spinners and dice). They should use common fractions to express probabilities that are neither certain nor impossible.

3. Important Terms Experiment – something that takes place for which what will happen is uncertain Outcome – a possible result Sample space – the set of all possible results Favorable – what we would like to see happen Unfavorable – what we would not like to see happen

4. Examples For each experiment below, find the sample space: 1.Rolling a fair die 2.Spinning the spinner shown below 3.Tossing a coin 4.Tossing two coins

5. Probability Ratio The probability that an event E occurs is the ratio of the number of ways that E can occur to the number of elements in the sample space S:

6. Examples A penny, a nickel, and a dime are tossed. Find the probability of getting exactly 2 heads. A green die and a red die are tossed. Find the probability that the sum is: a.7 b.Less than 4 c.13

7. More Examples A card is drawn from a standard deck of 52 playing cards. Find the probability that the card drawn is: a.Black b.The queen of diamonds c.A face card or a club d.A face card and a club

8. Yet More Examples Recall the age data from our previous class. a.What is the probability that a randomly selected person is legal drinking age in the state of Alabama? b.What is the probability that a randomly selected person is over 30, given that the person is of legal drinking age?

9. Almost Done One M&M is chosen at random. a.What is the probability that it is orange? b.What is the probability that it is yellow, given that it is a primary color? c.What is the probability that is a primary color, given that it is yellow? d.What is the probability that it is purple?

10. Modified Homework 1 – 10, 14, 16, 32, 34, 35, 36