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3.1 – Probability and Odds

3.1 – Probability and Odds. 3.1 – Probability and Odds. Today we will be learning about: Finding the probability 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.

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3.1 – Probability and Odds

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  1. 3.1 – Probability and Odds

  2. 3.1 – Probability and Odds • Today we will be learning about: • Finding the probability of an event • Finding the odds of an event

  3. 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

  4. 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.

  5. 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.

  6. 3.1 – Probability and Odds • Theoretical Probability P = Number of favorable outcomes Total number of outcomes

  7. 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

  8. 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?

  9. Type of company37 Salary-93 location-103 Size of company 17 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?”

  10. 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

  11. 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?

  12. 3.1 – 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?

  13. 3.1 – Probability and Odds • 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? • Probability of event occurring = [left side of odds/(left side of odds + right side of odds)] = 2/(2 + 1) = 2/3 • Probability of event not occurring = [right side of odds/(left side + right side)] = 1 – (probability of the event occurring)

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