2. 5, given that the number trati it is 3. An odd number, given that the number rolled was 3 four Cif two fair dice are rolled (recall the 36-outcome sample space), Jina the probability of rolling the given events. abil a fi оne 4. A sum of 8, given that the sum was greater than 7 bil 5. A sum of 6, given that the roll was a "double" (two identical numbers) 21 22 6. A double, given that the sum was 9 23 CIf two cards are drawn without replacement from an ordinary deck, find the probabilities of the given event. (See Example 7.) 7. The second is a heart, given that the first is a heart A 8. The second is black, given that the first is a spade 9. A jack and a 10 are drawn. 10. An ace and a 4 are drawn. 11. In your own words, explain how to find the conditional proba- bility P(EF). 12. Your friend asks you to explain how the product rule for inde- pendent events differs from the product rule for dependent events. How would you respond? 13. Another friend asks you to explain how to tell whether two events are dependent or independent. How would you reply? (Use your own words.) 14. A student reasons that the probability in Example 3 of both coins being heads is just the probability that the other coin is a head-that is, 1/2. Explain why this reasoning is wrong. Decide whether the two events listed are independent.
2. 5, given that the number trati it is 3. An odd number, given that the number rolled was 3 four Cif two fair dice are rolled (recall the 36-outcome sample space), Jina the probability of rolling the given events. abil a fi оne 4. A sum of 8, given that the sum was greater than 7 bil 5. A sum of 6, given that the roll was a "double" (two identical numbers) 21 22 6. A double, given that the sum was 9 23 CIf two cards are drawn without replacement from an ordinary deck, find the probabilities of the given event. (See Example 7.) 7. The second is a heart, given that the first is a heart A 8. The second is black, given that the first is a spade 9. A jack and a 10 are drawn. 10. An ace and a 4 are drawn. 11. In your own words, explain how to find the conditional proba- bility P(EF). 12. Your friend asks you to explain how the product rule for inde- pendent events differs from the product rule for dependent events. How would you respond? 13. Another friend asks you to explain how to tell whether two events are dependent or independent. How would you reply? (Use your own words.) 14. A student reasons that the probability in Example 3 of both coins being heads is just the probability that the other coin is a head-that is, 1/2. Explain why this reasoning is wrong. Decide whether the two events listed are independent.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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Transcribed Image Text:2. 5, given that the number
trati
it is
3. An odd number, given that the number rolled was 3
four
Cif two fair dice are rolled (recall the 36-outcome sample space), Jina
the probability of rolling the given events.
abil
a fi
оne
4. A sum of 8, given that the sum was greater than 7
bil
5. A sum of 6, given that the roll was a "double" (two identical
numbers)
21
22
6. A double, given that the sum was 9
23
CIf two cards are drawn without replacement from an ordinary deck,
find the probabilities of the given event. (See Example 7.)
7.
The second is a heart, given that the first is a heart
A
8. The second is black, given that the first is a spade
9. A jack and a 10 are drawn.
10. An ace and a 4 are drawn.
11. In your own words, explain how to find the conditional proba-
bility P(EF).
12. Your friend asks you to explain how the product rule for inde-
pendent events differs from the product rule for dependent
events. How would you respond?
13. Another friend asks you to explain how to tell whether two
events are dependent or independent. How would you reply?
(Use your own words.)
14. A student reasons that the probability in Example 3 of both
coins being heads is just the probability that the other coin is a
head-that is, 1/2. Explain why this reasoning is wrong.
Decide whether the two events listed are independent.
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