1. Section 5.4 - Conditional Probability P23. For the Titanic data in Display 5.39, let S be the event a person survived and F be the event a person was female. Find and interpret these probabilities. a.P(F) b.P(F|S) c.P(not F) d.P(not F|S) e.P(S|not F) Display 5.39 Gender MaleFemaleTotal Survived? Yes367344711 No13641261490 Total17314702201

2. Section 5.4 - Conditional Probability P23. Display 5.39 Gender MaleFemaleTotal Survived? Yes367344711 No13641261490 Total17314702201

3. Section 5.4 - Conditional Probability P24. Display 5.44 gives the hourly workers in the U.S., classified by race and by whether they were paid at or below minimum wage or above minimum wage. You select an hourly worker at random. a.Find P(at or Below) b.Find P(at or Below|White) c.What does a comparison of the two probabilities in parts a and b tell you? Race Paid at or Below Minimum Wage Paid Above Minimum Wage Total White1,68158,19659,877 Black2279,1909,417 Asian382,6342,672 Total1,94670,02071,966

4. Section 5.4 - Conditional Probability P24. Display 5.44 gives the hourly workers in the U.S., classified by race and by whether they were paid at or below minimum wage or above minimum wage. You select an hourly worker at random. a.Find P(at or Below) b.Find P(at or Below|White) c.What does a comparison of the two probabilities in parts a and b tell you? White workers are slightly more likely to be paid at or below minimal wage than workers in general. Race Paid at or Below Minimum Wage Paid Above Minimum Wage Total White1,68158,19659,877 Black2279,1909,417 Asian382,6342,672 Total1,94670,02071,966

5. Section 5.4 - Conditional Probability P24. Display 5.44 gives the hourly workers in the U.S., classified by race and by whether they were paid at or below minimum wage or above minimum wage. You select an hourly worker at random. d.Find P(Black) e.Find P(Black|at or Below) f.What does a comparison of the two probabilities in parts d and e tell you? Race Paid at or Below Minimum Wage Paid Above Minimum Wage Total White1,68158,19659,877 Black2279,1909,417 Asian382,6342,672 Total1,94670,02071,966

6. Section 5.4 - Conditional Probability P24. Display 5.44 gives the hourly workers in the U.S., classified by race and by whether they were paid at or below minimum wage or above minimum wage. You select an hourly worker at random. d.Find P(Black) e.Find P(Black|at or Below) f.What does a comparison of the two probabilities in parts d and e tell you? A worker who is paid at or below minimum wage is less likely to be black than a worker selected at random. Race Paid at or Below Minimum Wage Paid Above Minimum Wage Total White1,68158,19659,877 Black2279,1909,417 Asian382,6342,672 Total1,94670,02071,966

7. Section 5.4 - Conditional Probability P25.Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities. a.P(2nd is red|1st is red) b.P(2nd is red|1st is blue) c.P(3rd is blue|1st is red and 2nd is blue) d.P(3rd is red|1st is red and 2nd is red)

8. Section 5.4 - Conditional Probability P25.Suppose Jack draws marbles at random, without replacement, from a bag containing three red and two blue marbles. Find these conditional probabilities.

9. Section 5.4 - Conditional Probability P26. Suppose Jill draws a card from a standard 52-card deck. Find the probability that a.It is a club, given that it is black. b.It is a jack, given that it is a heart. c.It is a heart, given that it is a jack.

10. Section 5.4 - Conditional Probability P26. Suppose Jill draws a card from a standard 52-card deck. Find the probability that a.It is a club, given that it is black. b.It is a jack, given that it is a heart. c.It is a heart, given that it is a jack.

11. Section 5.4 - Conditional Probability P27. Look again at the Titanic data in Display 5.39. Make a tree diagram to illustrate this situation, this time branching first on whether the person survived. Write these probabilities as unreduced fractions. P(S); P(F|S); P(S and F) Display 5.39 Gender MaleFemaleTotal Survived? Yes367344711 No13641261490 Total17314702201

12. Section 5.4 - Conditional Probability Make a tree diagram to illustrate this situation, this time branching first on whether the person survived.

13. Section 5.4 - Conditional Probability Write a formula that tells how the three probabilities in part b are related. Compare it to the computation on p 328.

14. Section 5.4 - Conditional Probability Write a formula that tells how the three probabilities in part b are related. Compare it to the computation on p 328.

15. Section 5.4 - Conditional Probability P28. Use the Multiplication Rule to find the probability that if you draw two cards from a deck without replacing the first before drawing the second, both cards will be hearts. What is the probability if you replace the first card before drawing the replacement?

16. Section 5.4 - Conditional Probability P28. Use the Multiplication Rule to find the probability that if you draw two cards from a deck without replacing the first before drawing the second, both cards will be hearts. What is the probability if you replace the first card before drawing the replacement?

17. Section 5.4 - Conditional Probability P29. Suppose you take a random sample of size n = 2, without replacement, from the population {W,W,M,M}. Find these probabilities: P(W chosen 1st) P(W chosen 2nd|W chosen 1st) P(W chosen 1st and W chosen 2nd)

18. Section 5.4 - Conditional Probability P29. Suppose you take a random sample of size n = 2, without replacement, from the population {W,W,M,M}. Find these probabilities:

19. Section 5.4 - Conditional Probability P30. Use the Multiplication Rule to find the probability of getting a sum of 8 and doubles when you roll two dice.

20. Section 5.4 - Conditional Probability P30. Use the Multiplication Rule to find the probability of getting a sum of 8 and doubles when you roll two dice.

21. Section 5.4 - Conditional Probability P31. Suppose you roll two dice. Use the definition of conditional probability to find P(D|8). Compare this probability with P(8|D).

22. Section 5.4 - Conditional Probability P31. Suppose you roll two dice. Use the definition of conditional probability to find P(D|8). Compare this probability with P(8|D).

23. Section 5.4 - Conditional Probability P32. Suppose you know that, in a class of 30 students, 10 students have blue eyes and 20 students have brown eyes. Twenty-four of the students are right-handed, and 6 are left- handed. Of the left-handers, 2 have blue eyes. Make a two- way table showing this situation. Then use the definition of conditional probability to find the probability that a student randomly selected from this class is right-handed, given that the student has brown eyes.

24. Section 5.4 - Conditional Probability P32. Suppose you know that, in a class of 30 students, 10 students have blue eyes and 20 students have brown eyes. Twenty-four of the students are right-handed, and 6 are left- handed. Of the left-handers, 2 have blue eyes. Make a two- way table showing this situation. Then use the definition of conditional probability to find the probability that a student randomly selected from this class is right-handed, given that the student has brown eyes. Right-HandedLeft-HandedTotal Blue Eyes8210 Brown Eyes16420 Total24630

25. Section 5.4 - Conditional Probability P33. As of July 1 of a recent season, the L.A. Dodgers had won 53% of their games. 18% of their games had been played against left-handed starting pitchers. The Dodgers won 36% of the games played against left-handed starting pitchers. What percentage of their games against right-handed starting pitchers did they win?

26. Section 5.4 - Conditional Probability P33. As of July 1 of a recent season, the L.A. Dodgers had won 53% of their games. 18% of their games had been played against left-handed starting pitchers. The Dodgers won 36% of the games played against left-handed starting pitchers. What percentage of their games against right-handed starting pitchers did they win? For a typical set of 100 games, the W-L record would look approximately like the following table: Right-Handed PitcherLeft-Handed PitcherTotal Won46.526.48 =.36 x 1853 Lost35.4811.5247 Total8218100