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Probability and Odds in Counting | Practical Examples and Calculations

Learn about probability, including theoretical and experimental probability, favorable outcomes, event likelihood, and odds calculation. Explore practical examples with clear explanations and calculations to enhance your understanding of probability concepts.

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Probability and Odds in Counting | Practical Examples and Calculations

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  1. Counting and Probability Lesson 5- Probability and Odds

  2. 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. 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.

  4. 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.

  5. Probability and Odds • Theoretical Probability P(event) = Number of favorable outcomes Total number of outcomes

  6. 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

  7. 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?

  8. 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?”

  9. 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

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

  11. 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?

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