3.1 – Probability and Odds

Today we will be learning about: Today we will be learning about: Finding the probability of an event Finding the probability of an event Finding the odds of an event Finding the odds of an event

3.1 – Probability and Odds Probability of an event – measure of the likelihood that the event will occur. It is a number between 0 and 1

3.1 – 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.

3.1 – 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.

3.1 – Probability and Odds Theoretical Probability P = Number of favorable outcomes Total number of outcomes

3.1 – 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

3.1 – 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?

3.1 – 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 company 37 Size of company 17

3.1 – 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

3.1 – Probability and Odds Example 3 You randomly choose a letter from the word SUMMER. What are the odds that the letter is a vowel?

3.1 – Probability and Odds Example 4 The probability that a randomly chosen 4 digit security code contains at least one zero is What are the odds that a 4 digit security code contains at least one zero?

3.1 – Probability and Odds Ex.5 – Given the odds, find the probability. Ex.5 – Given the odds, find the probability. The odds of rolling a number greater than 2, on a die, are 2:1. What is the probability of rolling a number greater than 2? The odds of rolling a number greater than 2, on a die, are 2:1. What is the probability of rolling a number greater than 2? Probability of event occurring = [left side of odds/(left side of odds + right side of odds)] Probability of event occurring = [left side of odds/(left side of odds + right side of odds)] = 2/(2 + 1) = 2/3 = 2/(2 + 1) = 2/3 Probability of event not occurring = [right side of odds/(left side + right side)] = Probability of event not occurring = [right side of odds/(left side + right side)] = 1 – (probability of the event occurring) 1 – (probability of the event occurring)