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Chapter 2 – Properties of Chapter 2 – Properties of Real NumbersReal Numbers
2.8 – Probability and Odds2.8 – Probability and Odds
2.8 – Probability and Odds2.8 – Probability and Odds
Today we will be learning about:Today we will be learning about: Finding the probability of an eventFinding the probability of an event
Finding the odds of an eventFinding the odds of an event
2.8 – Probability and Odds2.8 – Probability and Odds
Probability of an event – measure of the likelihood that the event will occur. It is a number between 0 and 1
2.8 – Probability and Odds2.8 – Probability and Odds
Outcomes – different possible results When an event has N equally likely outcomes,
each of them occur with probability 1/N. Example: Rolling a six-sided number cube, the
possible outcomes are 1, 2, 3, 4, 5, and 6. The probability associated with each outcome is 1/6.
2.8 – Probability and Odds2.8 – Probability and Odds
EVENT – all of the possible outcomes In the roll of a six-sided number cube, an “even
roll” consists of the outcomes 2, 4, and 6. THEORETICAL PROBABILITY - the
probability that should happen. The theoretical probability of an even roll is 3/6 =
½. FAVORABLE OUTCOMES – the outcomes
you wish to have happen.
2.8 – Probability and Odds2.8 – Probability and Odds
Theoretical Probability P =
Number of favorable outcomes
Total number of outcomes
2.8 – Probability and Odds2.8 – Probability and Odds
Another type of probability is EXPERIMENTAL PROBABILITY. This type of probability is based on repetitions of an actual experiment and is calculated by the following rule.
Experimental probability P = Number of favorable outcomes observed
Total number of trials
2.8 – Probability and Odds2.8 – Probability and Odds
Example 1 You have 2 red and 2 black socks in a drawer.
You reach in and pick two without looking. What is the probability P that they do not match
In a group of students, 12 ride the bus to school, 8 are driven to school, and 5 walk. One of the students is chosen at random from the group. What is the probability P that the student walks to school?
2.8 – Probability and Odds2.8 – Probability and Odds
Example 2 Use the circle graph below showing the responses of 250
college students to a survey asking “Which factor is most likely to influence your job choice after graduation?” If you were to ask a randomly chosen college student this question, what is the experimental probability that the student would say “type of company?”
Salary-93
location-103
Type of company37
Size of company
17
2.8 – Probability and Odds2.8 – Probability and Odds
THE ODDS OF AN EVENT When all outcomes are equally likely, the ODDS
that an event will occur are given by the formula: ODDS = Number of favorable outcomes
Number of unfavorable outcomes
2.8 – Probability and Odds2.8 – Probability and Odds
Example 3 You randomly choose a letter from the word
SUMMER. What are the odds that the letter is a vowel?
2.8 – Probability and Odds2.8 – Probability and Odds
Example 4 The probability that a randomly chosen 4 digit
security code contains at least one zero is 0.34. What are the odds that a 4 digit security code contains at least one zero?
2.8 – Probability and Odds2.8 – Probability and Odds
HOMEWORK
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