1 / 15

Being Equally Likely

Being Equally Likely. Ellie Qu. Home. One event, all outcomes equally likely . Games. What is a venn diagram?. Probability Rules. What is sample space?. Step One.

manon
Download Presentation

Being Equally Likely

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. Being Equally Likely Ellie Qu

  2. Home One event, all outcomes equally likely Games • What is a venn diagram? • Probability Rules • What is sample space? Step One

  3. Example: For instance, when you roll a pair of dice, you might ask how likely you are to rolla seven. Then you are asking what is the probability to roll a seven. What is Probability ? Note: The probability of an occurance of an event can be expressed as a fraction or a decimal between 0 and 1. Definition: The study of probability helps us figure out the likelihood of something happening. What is Sample Space?

  4. Example: For example, if the probability of picking a redmarble from a jar that contains 4 red marblesand 6 blue marbles is 4/10 or 2/5, then theprobability of not picking a red marble is equalto 1 - 4/10 = 6/10 or 3/5, which is also theprobability of picking a blue marble. That is,given this example, the probability of picking a red marble plus the probability of picking ablue marble will equal 1 (or 100 percent). Inthis, case, 10 is the sample space. What is Sample Space ? Definition: The sample space is a set consisting of all the possible outcomes of an event. Equally Likely Outcomes

  5. Example: Suppose we have ten marbles, 4 red and 6 blue. What is the probability if we picked a red marble without looking? (4/10) What is the probability if we picked a blue marble without looking? (6/10) Conclusion: The probability of picking any red marble is equally likely, and the probability of picking any blue is equally likely. equally likely outcomes Definition: Any individual has the same chance of being chosen. Probability Rules

  6. Rule 2: The sum of all the probabilities in the sample space is 1. Rule 3: The probability of an event which cannot occur is 0. Rule 4: The probability of an event not occurring is one minus the probability of it occurring: P(E') = 1 - P(E) What is Probability Rules? Rule 1: All probabilities are between 0 and 1 inclusive: 0 <= P(E) <= 1 What is a Venn Diagram

  7. Example: Below is a venn diagram. A and B are events in a sample space, S. The intersection of A and B is written as : P(A and B). The union of A and B is written as : P(A or B). What is A Venn Diagram? Definition: A Venn Diagram describes the probabilities of different events graphically. Examples of Venn Diagram

  8. P(A and B) = P(A) . P(B) P(A) = 1/2 P(B) = 1/2P(A and B) = 1/2 . 1/2 = 1/4 Examples using a vein diagram • Given: Suppose a high school consists of 25% juniors,15% seniors, and the remaining 60% is students of other grades. The relative frequency of students who are either juniors and seniors is 40%. Given: What is the probability that two tails occurs when two coins are tossed? Let A represent the occurrence of a tail on the first coin and B represent the occurrence of a tail on the second coin. P(A or B) = P(A) + P(B) P(J or S) = 0.25 + 0.15 which equals 0.40 Application problems

  9. Application Problems • #1 What is the probability of drawing one ace and then another ace from a deck of playing cards? Next problem Answer Hint

  10. Application Problems • Suppose we have two dice. A is the event that 4 shows on the first die, and B is the event that 4 shows on the second die. If both dice are rolled at once, what is the probability that two 4s occur? Previous Problem Hint Answer

  11. Hint: First die: 1/6 second die: 1/6 Go back to problem Go to Answer

  12. P(A) = 1/6P(B) = 1/6P(A and B) = P(A) . P(B) = 1/6 . 1/6 = 1/36 Answer: Go back to problem Go to Games

  13. Since there are 4 aces in a 52 deck of cards, the probability of drawing one ace is 4/52. After the first draw, the 51 cards remaining contain 3 aces and therefore the probability of drawing an ace on the second draw is 3/51. Hint: Go back to problem

  14. Answer: 4/52 . 3/51 = 1/221 Go back to problem Go to the next problem

  15. Links to Probability Games Coin Flip, Dice Roll: http://www.betweenwaters.com/probab/probab.html Application games: http://www.bbc.co.uk/skillswise/numbers/handlingdata/probability/game.shtml MathHelp Notebook on Probability: http://www.ucl.ac.uk/Mathematics/geomath/level2/prob/MHpb.html

More Related