1 / 66

Ice Cream Preferences and Basic Probability

Explore ice cream preferences based on a survey and learn about basic probability concepts. Calculate probabilities of different outcomes and understand the concepts of independent and dependent events.

lal
Download Presentation

Ice Cream Preferences and Basic Probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Thursday 05/16 Warm Up 200 people were surveyed about ice cream preferences. 78 people said they prefer chocolate. 65 people said they prefer strawberry. The rest prefer vanilla. • What percentage of people prefer chocolate? • What percentage of people prefer vanilla?

  2. Basic Probability Probability is the science or study of the chances of an event occuring.

  3. Examples of probability in the real world Can you think of anymore?

  4. The scale of probability Impossible- never could happen Unlikely- probably won’t happen Sometimes- maybe, equal chance More likely- probably will Certain- always, for sure!

  5. Example: Determine the scale of probability of an event happening. • The spinner landing on green? • The spinner landing on yellow? • The spinner landing on blue? • The spinner landing on a color?

  6. Sample Space A sample space is a set of all possible outcomes. What would be the sample space of… • A six sided die? • Flipping a coin? • Flipping three coins?

  7. Determining Basic Probability

  8. Examples If the wheel has all of your names, plus your teachers name, what is the probability your name will be selected?

  9. Examples You have a basket of eggs with 4 pink eggs, 5 green eggs, 6 yellow eggs, and 2 blue eggs. What is the probability of pulling out a green egg? P(G) What is the probability of pulling out an egg that is not pink? P(notP) What is the probability of pulling out a blue egg? P(B)

  10. Examples I have a six sided die. What is the probability I roll a 4? What is the probability I roll an even number? What is the probability I roll a number that is not 3?

  11. Task 9.1 TB or Not TB? Find the following probabilities • A person has TB • A person does not have TB • A person has TB and tests positive • A person has TB and test negative • A person doesn’t have TB and test positive • A person doesn’t have TB and test negative

  12. Friday 05/17 Warm Up Open your booklets to page 3. Answer questions #1-5 on your warm up sheet.

  13. Task 9.2 Page 5

  14. Experimental probability is the probability of something happening based off of actual experimental data.

  15. Experimental Probability

  16. Experiment Time! We are going to roll a die 15 times and record our data. Then find the following: • P(1) • P(5 or 6) • P(odd number) • P(even number) • P(a number divisible by 3)

  17. Experiment Time! We’ve got a basket of 20 eggs. We will record our data. Then find the following: • P(green) • P(blue) • P(not pink) • P(blue or yellow)

  18. Exit Ticket Complete the Two-Way Table

  19. Monday 05/20 Warm Up Open your booklets to page 7. Answer questions #1-4 on your warm up sheet.

  20. Events are independent events if the occurrence of one event does not affect the probability of the other.

  21. Independent Events If A and B are independent events, then P(A and B)= P(A) • P(B)

  22. Example 1 Find the probability of flipping a coin twice and it landing on Heads both times. **Is flipping a coin an independent event?** YES The outcome of one toss does not affect the probability of heads on the other toss There are two ways to solve this: Draw a tree diagram Answer with multiplication

  23. Example 2 A six-sided cube is labeled with the numbers 1, 2, 2, 3, 3, and 3. Four sides are colored red, one side is white and one side is yellow. Find the probability. • Tossing 2, then 2 • Tossing red, then white, then yellow.

  24. Events are dependent events if the occurrence of one event affects the probability of the other.

  25. Dependent Events If A and B are dependent events, then P(A and B) = P(A) • P(B | A) Where P(A | B) is the probability of B, given that A has occurred.

  26. Example 1 There are 2 lemons and 1 lime in a bag. If you pull out two pieces of fruit, the probability change depending on the outcome of the first. • P(2 lemons) • P(lime, then lemon)

  27. Example 2 Two number cubes are rolled - one red, and one blue. Explain why the events are dependent. Then find the indicated probability. The red cube shows a 1, and the sum is less than 4.

  28. You Try! Two cards are drawn from a deck of 52. Determine whether the events are independent or dependent. Find the probability. • Selecting two hearts when the first card is replaced • Selecting two hearts when the first card is not replaced • A queen is drawn, is not replaced, and then a king is drawn

  29. Homework: pg. 7 and pg. 8 #6-13

  30. Tuesday 05/21 Warm Up Open your booklets to page 14. Answers questions #1-5 on your warm up sheet

  31. Check Homework: pg. 7 and pg. 8 #6-13

  32. The conditional probability of an event B, in relation to event A, is the probability that event B will occur given the knowledge that an event A has already occurred

  33. The probability is written P(B | A), notation for the probability of B given A

  34. Conditional Probability We need to revisit our previous discussion of independent and dependent events.

  35. Example Two colored dice (one white, one red) are rolled. • What is the probability of rolling “box cars” (two sixes)? • What is the probability of rolling “box cars” knowing the first toss is a six?

  36. Conditional Probablity If events A and B are dependent (where A has effect on the probability of event B), then we saw that the probability that both events occur is defined by P(A and B) = P(A) • P(B | A)

  37. Conditional Probablity Dividing both sides of this equation by P(A) gives us our formula for conditional probability of event B given event A, where event A affects the probability of event B:

  38. Example A bag contains 12 red M&Ms, 12 blue M&Ms, and 12 green M&Ms. What is the probability of drawing two M&Ms of the same color in a row?

  39. Example In a school of 1200 students, 250 are seniors, 150 students take math, and 40 students are seniors and are also taking math. What is the probability that a randomly chosen student who is a senior, is taking math?

  40. Task 9.3

  41. Homework: page 15 #8-15

  42. Wednesday 05/22 Warm Up Open your booklets to page 18. Answer questions #1-8 on your warm up sheet.

  43. Check Homework: page 15 #8-15

  44. Probability Games

  45. Homework: Quiz PRactice Problems and pg. 18 #9 ONLY

  46. Thursday 05/23 Warm Up Open your booklets to page 17. Answer questions #1, 2a and 2b on your warm up sheet.

  47. Check Homework: Quiz PRactice Problems and pg. 18 #9 ONLY

  48. Quiz Day!

  49. Friday 05/24 Warm Up Open your booklets to page 29. Answer questions #13 - 15

  50. A simple event is an event that describes a single outcome

More Related