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Counting and Probability. Lesson 5- Probability and Odds. Probability and Odds. Probability of an event – measure of the likelihood that the event will occur. It is a number between 0 and 1. Probability and Odds. Outcomes – different possible results
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Counting and Probability Lesson 5- Probability and Odds
Probability and Odds • Probability of an event – measure of the likelihood that the event will occur. • It is a number between 0 and 1
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.
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.
Probability and Odds • Theoretical Probability P(event) = Number of favorable outcomes Total number of outcomes
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(event)= Number of favorable outcomes observed Total number of trials
Probability and Odds • Example 1 • You have 6 red and 12 black socks in a drawer. You reach in and pick a sock without looking. What is the probability P that the sock you pick in NOT black? • 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?
Type of company37 Salary-93 location-103 Size of company 17 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?”
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 Odds vs. Probability
Probability and Odds • Example 3 • You randomly choose a letter from the word SUMMER. What are the odds that the letter is a vowel?
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?