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Probability and Chance

Probability and Chance. Probability. If it is uncertain whether or not an event will happen, then its probability is some fraction (or decimal) between 0 and 1. All of the probabilities related to a particular situation must add up to 100% or 1.0 in decimal form. Example: Classroom

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Probability and Chance

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  1. Probability and Chance

  2. Probability If it is uncertain whether or not an event will happen, then its probability is some fraction (or decimal) between 0 and 1.

  3. All of the probabilities related to a particular situation must add up to 100% or 1.0 in decimal form. Example: Classroom P (picking a boy) = 0.60 P (picking a girl) = ____ 0.40 1.00

  4. What is the probability that the spinner will stop on part A? A B D C • What is the probability that the spinner will stop on: • An even number? • An odd number? C 3 A 1 B 2 What is the probability that the spinner will stop in the area marked A?

  5. 1 3 = = 2 6 You roll a six-sided die whose sides are numbered from 1 through 6. What is the probability of rolling an ODD number? There are 3 ways to roll an odd number: 1, 3, 5. P

  6. Donald is rolling a dice labeled 1 to 6. Which of the following is LEAST LIKELY? • an even number • an odd number • a number greater than 5

  7. Probability Activity With your elbow partner, open the M&M bag and put the candy on the paper plate. Make a table of how many of each color M&M you have. Answer the following questions: • Which color you are more likely to pull out? • Least likely? Unlikely? Equally likely? • What is the probability of getting a brown M&M? • What is the probability of getting a yellow M&M? • Make up your own problem with the M&Ms.

  8. Probability Questions Lawrence is the captain of his track team. The team is deciding on a color and all eight members wrote their choice down on equal size cards. If Lawrence picks one card at random, what is the probability that he will pick blue? blue blue green black yellow blue black red

  9. CHANCE Chance is how likely it is that something will happen. To state a chance, we use a percent. ½ Probability 0 1 Equally likely to happen or not to happen Certain to happen Certain not to happen Chance 50 % 0% 100%

  10. Chance When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to rain. If the chance drops to 20%, then it may rain, but it probably will not rain.

  11. Chance What is the chance of spinning a number greater than 1? What is the chance of spinning a 4? What is the chance that the spinner will stop on an odd number? What is the chance of rolling an even number with one toss of on number cube? 2 1 3 4

  12. Vocabulary • A compound event combines two or more events, using the word and or the word or. • If two or more events cannot occur at the same time they are termed mutually exclusive (disjoint). • They have no common outcomes. • Overlappingevents have at least one common outcome. • Two events are independent if the occurrence of one event has no effect on the other • Two events are dependent if the occurrence of one event affects the outcome of the other

  13. Mutually Exclusive Events • The probability is found by adding the individual probabilities of the events: • P(A or B) = P(A) + P(B) • A Venn diagram is used to show mutually exclusive events.

  14. Mutually Exclusive Events • Example 1: • Find the probability that a girl’s favorite department store is Macy’s or Nordstrom. • Find the probability that a girl’s favorite store is not JC Penny’s. 0.45 0.90

  15. Mutually Exclusive Events • Example 2: • When rolling two dice, what is probability that your sum will be 4 or 5? 7/36

  16. Mutually Exclusive Events • Example 3: • What is the probability of picking a queen or an ace from a deck of cards 2/13

  17. Overlapping Events • Probability that overlapping events A and B or both will occur expressed as: • P(M or E) = P(M) + P(E) - P(ME)

  18. Overlapping Events • Example 1: • Find the probability of picking a king or a club in a deck of cards. 4/13

  19. Overlapping Events • Example 2: • Find the probability of picking a female or a person from Tennessee out of the committee members.

  20. Overlapping Events • Example 3: • When rolling 2 dice, what is the probability of getting an even sum or a number greater than 10?

  21. You Try… • 100 people were asked their favorite fast food restaurant. The table below has the information from the survey: • What is the probability that a person likes Wendy’s? • What is the probability that a person is male given they like Burger King? • 3. What is the probability that a person is female or likes McDonald’s? 7/20 3/5 3/4

  22. What’s the difference?

  23. Independent Events

  24. Experiment 1 A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and a yellow marble?

  25. Dependent Events

  26. Experiment 2 A random sample of parts coming off a machine is done by an inspector. He found that 5 out of 100 parts are bad on average. If he were to do a new sample, what is the probability that he picks a bad part and then picks another bad part if he doesn’t replace the first?

  27. TOTD Answer the following 2-part question before you leave: • A basket of apples contains 11 apples – 6 are red, 2 are green, and 3 are yellow. You randomly select 2 apples, one at a time. Find the probability that both are yellow if • You replace the first apple, then select the second • You eat the first apple, then select the second.

  28. Homework: Pg. 353 1 - 8

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