Exercises 135a. What is the probability that you will win the grand prize?
b. What is the probability that your brother will win?
c. What is the probability that you or your brother will win?5.3 Assume the same situation as in Exercise 5.2, except that a total of only 10 tickets were sold
and that there are two prizes.
a. Given that you don’t win first prize, what is the probability that you will win second
prize? (The first prize-winning ticket is not put back in the hopper.)
b. What is the probability that your brother will win first prize and you will win second
prize?
c. What is the probability that you will win first prize and your brother will win second
prize?
d. What is the probability that the two of you will win the first and second prizes?
5.4 Which parts of Exercise 5.3 deal with joint probabilities?
5.5 Which parts of Exercise 5.3 deal with conditional probabilities?
5.6 Make up a simple example of a situation in which you are interested in joint probabilities.
5.7 Make up a simple example of a situation in which you are interested in conditional proba-
bilities.
5.8 In some homes, a mother’s behavior seems to be independent of her baby’s, and vice versa.
If the mother looks at her child a total of 2 hours each day, and the baby looks at the mother
a total of 3 hours each day, and if they really do behave independently, what is the probabil-
ity that they will look at each other at the same time?
5.9 In Exercise 5.8, assume that both the mother and child are asleep from 8:00P.M. to 7:00A.M.
What would the probability be now?
5.10 In the example dealing with what happens to supermarket fliers, we found that the probabil-
ity that a flier carrying a “do not litter” message would end up in the trash, if what people
do with fliers is independent of the message that is on them, was .033. I also said that 4.5%
of those messages actually ended up in the trash. What does this tell you about the effective-
ness of messages?
5.11 Give an example of a common continuous distribution for which we have some real interest
in the probability that an observation will fall within some specified interval.
5.12 Give an example of a continuous variable that we routinely treat as if it were discrete.
5.13 Give two examples of discrete variables.
5.14 A graduate-admissions committee has finally come to realize that it cannot make valid dis-
tinctions among the top applicants. This year, the committee rated all 300 applicants and
randomly chose 10 from those in the top 20%. What is the probability that any particular
applicant will be admitted (assuming you have no knowledge of her or his rating)?
5.15 With respect to Exercise 5.14,
a. What is the conditional probability that a person will be admitted given that she has the
highest faculty rating among the 300 students?
b. What is the conditional probability given that she has the lowest rating?5.16 Using Appendix Data Set or the file ADD.dat on the Web site,
a. What is the probability that a person drawn at random will have an ADDSC score
greater than 50 if the scores are normally distributed with a mean of 52.6 and a stan-
dard deviation of 12.4?
b. What percentage of the sample actually exceeded 50?