Beginners counting and probability.pptx
- 6. Homework Review How many positive integers less than 200 are divisible by 2, 3 and 5? ● 6 positive integers List the factors for 81 ● 1, 3, 9, 27, 81
- 7. Definition of Sample Space The sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment. For example, if you roll a dice, 6 things could happen. You could roll a 1, 2, 3, 4, 5, or 6. Therefore, 1, 2, 3, 4, 5, and 6 would be the sample space for this experiment.
- 8. Tree Diagram As we all know, you can have two possible outcomes when flipping a coin 1 time: heads or tails. But how would we find the possible outcomes when we flip a coin 3 times? We can find the sample space using a tree diagram:
- 9. Listing the possibilities: Another way to find the possible outcomes is to list them. Say we have two dices and we roll them at the same time. What are all the possible results that we can get? We can find the sample space using a chart:
- 10. Practice Problem
- 11. Answer
- 12. Definition of Counting Principle The Fundamental Counting Principle is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes
- 13. The Counting Principle ... Question: How many different possible breakfast combinations are there if you order one from each group: EGG GROUP ( Scrambled eggs, Fried Eggs, Omelette ) MEAT GROUP ( Bacon, Sausage )
- 14. Answer: ... Since there are 3 possible egg choices and 2 possible meat choices, we can apply the counting principle and do 3 x 2 = 6
- 16. Answer: ...
- 17. Practice Problems (you don’t have to give an exact answer, showing the equation is enough): ...
- 18. Answer: 30 x 29 x 28 combinations possible 24 x 23 x 22 x 21 x 20 choices
- 19. Practice Problem
- 20. Answer
- 21. Definition of Probability Probability is the extent to which something is probable; the likelihood of something happening or being the case.
- 22. Finding The Probability Question: What is the probability of getting a head when flipping a coin one time?
- 23. Practice Problems: What is the probability of the following happening? 1. Randomly selecting the letter A in Cheatham? 1. Choosing a blue marble out of a bag filled with 3 blue marbles, 4 red marbles and 2 yellow marbles? 1. Throwing a fair coin 2 times and getting 2 heads?
- 24. Answer: What is the probability of the following happening? 1. 2/8, or 1/4 1. 3/9, or or 1/3 1. The total outcomes of throwing 2 heads: 2 x 2 = 4 The sample space of these 4 outcomes: (HH, HT, TH, TT) Therefore, the possibility of getting two heads (HH) is 1/4
- 25. Probability Restrictions The probability of an event occurring must be between 0 and 1, inclusive. An event that is for sure to happen will have a probability of 1. An event that cannot happen will have a probability of 0. The sum of the probabilities for all possible outcomes is equal to 1.
- 26. Practice Problems: What is the probability of the following happening? 1. Picking a candy that is not red out of a bag filled with 5 blue candies, 6 purple candies and 4 red candies? 2. Rolling a six-sided die and getting a number over 2? 3. Rolling two six-sided dice and getting a 3 and a 6?
- 27. Answer What is the probability of the following happening? 1. 11/15 2. 2/3 3. 1/18
- 28. Review Problem:
- 29. Answer
- 30. Review Problem To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
- 31. Answer A customer can choose one monitor, one keyboard, one computer and one printer. The diagram below shows each item with the number of choices the customer has. Using the counting principle, the number of all possible choices can be found by 4 × 2 × 4 × 3 = 96
- 32. Time for handouts! Take the handouts that you printed out at home and using the concepts that we learned today, start working on them. If you don’t finish that’s okay, you can finish it at home.