2. Probability: Living with the Odds
Discussion Paragraph 7A
1 web
70. Blood Groups
71. Accidents
1 world
72. Probability in the News
73. Probability in your Life
74. Gambling Odds
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3. Combining Probabilities
Unit 7B
Combining Probabilities
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4. And Probability: Independent Events
Two events are independent if the outcome of one
does not affect the probability of the other event.
If two independent events A and B have individual
probabilities P(A) and P(B), the probability that A
and B occur together is P(A and B) = P(A) • P(B).
This principle can be extended to any number of
independent events.
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5. Consecutive Floods CN (1)
1. Find the probability that a 100-year flood (a flood with a .01 probability of striking in a given year) will strike a city in two consecutive years.
Assume that ta flood in one year does not affect the likelihood of a flood in the next year.
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6. Three Coins CN (2) Suppose you toss three coins.
2. What is the probability of getting three tails?
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7. And Probability: Dependent Events
Two events are dependent if the outcome of one affects the probability of the other event.
The probability that dependent events A and B occur together is
P(A and B) = P(A) • P(B given A)
where P(B given A) is the probability of event B given the occurrence of event A.
This principle can be extended to any number of
dependent events.
Help students understand that dependent events are those whose outcomes can be influenced by prior events. Practice makes perfect here.
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8. Bingo CN (3)
The game of Bingo involves drawing labeled buttons from a bin at random, without replacement. There are 75 buttons, 15 for each of the letters B, I, N, B, and O.
3. What is the probability of drawing two B buttons in the first two selections?
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9. Jury Selection CN (4)
A three-person jury must be selected at random from a pool of 12 people that has 6 men and 6 women.
4. What is the probability of selecting an all-male jury?
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10. Either/Or Probabilities: Non-Overlapping Events
Two events are non-overlapping if they cannot occur together, like the outcome of a coin toss, as shown to the right.
For non-overlapping events A and B, the probability that either A or B occurs is shown below.
P(A or B) = P(A) + P(B)
This principle can be extended to any number of
non-overlapping events.
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11. Either/Or Dice CN (5) Suppose you roll a single die.
5. What is the probability of rolling either a 2 or a 3?
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12. Either/Or Probabilities: Overlapping Events
Two events are overlapping if they can occur together, like the outcome of picking a queen or a club, as shown to the right.
For overlapping events A and B, the probability that either A or B occurs is shown below.
P(A or B) = P(A) + P(B) – P(A and B)
This principle can be extended to any number of
overlapping events.
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13. Democrats and Women CN (6)
You select one person at random from a room with eight people: two Democratic men, two Republican men, two Democratic women, and two Republican women.
6. What is the probability that you will select either a woman or a Democrat?
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14. Examples
What is the probability of rolling either a 3 or a 4 on a single six-sided die?
These are non-overlapping events.
P(A or B) = P(A) + P(B)
P(3 or 4) = P(3) + P(4) = 1/6 + 1/6 = 2/6 = 1/3
What is the probability that in a standard shuffled deck of cards you will draw a 5 or a spade?
These are overlapping events.
P(A or B) = P(A) + P(B) – P(A and B)
P(5 or spade) = P(5) + P(spade) – P(5 and spade)
= 4/ /52 – 1/52 = 16/52 = 4/13
Here the focus should be on determining if there is overlap in event outcomes.
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15. The At Least Once Rule (For Independent Events)
Suppose the probability of an event A occurring in one trial is P(A). If all trials are independent, the probability that event A occurs at least once in n trials is shown below.
P(at least one event A in n trials)
= 1 – P(not event A in n trials)
= 1 – [P(not A in one trial)]n
This particular example can be verified quite easily with a look at the sample space of four children. Ask other similar questions to assess students’ understanding of the rule.
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16. 100 Year Flood CN (7)
7. What is the probability that a region will experience at least one 100-year flood (a flood that has a .01 chance of occurring in any given year) during the next 100 years?
Assume that 100-year floods in consecutive years are independent events.
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17. Lottery Chances CN (8)
You purchase 10 lottery tickets, for which the probability of winning some prize on a single ticket is 1 in 10.
8. What is the probability that you will have at least one winning ticket among the 10 tickets?
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18. Quick Quiz CN (9)
9. Please answer the 10 quick quiz multiple choice questions on p. 435.
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19. Homework 7B Discussion Paragraph 7A Class Notes 1-9 p. 436: 1-10 1 web
59. Lottery Chances
60. HIV Probabilities
1 world
61. Combined Probability in the News
62. Combined Probability in Your Life
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