# Chapter 4: Student Exercises

5. For each problem below, how many ways can *n* objects can be selected from* N*?

6. Find the number of permutations of *n* objects selected from *N* objects.

15. Consider the experiment of rolling a pair of dice. Suppose we are interested in the *sum of the face values* showing on the dice.

17. An experiment consists of casting a single die; the sample space is* S* = {1, 2, 3, 4, 5, 6} Define 3 events: *A* = {1, 2}, *B* = {3, 4}, and *C* = {2, 3, 5, 6}.

18. Suppose that we have an experiment with the sample space comprised of 7 equally- likely sample points, *S* = {S1, S2, S3, S4, S5, S6, S7}. De ne 3 events in the following way:* A *= {S1, S4, S6}, *B* = {S2, S4, S7}, and *C* = {S2, S3, S5, S7}

19. An experiment consists of the roll of a single die; the sample space is *S* = {1, 2, 3, 4, 5, 6}. Define two events: *A *= {1, 3, 5} and* B* = {3, 4, 5}.

21. Suppose we have two events *A* and *B* with *p(A)* = 0.40 and *p(B)* = 0.20; the probability of the intersection of these two events is 0.10.

22. Suppose we have two events* A *and* B* with *p(A)* = 0.40 and* p(B) *= 0.20; the conditional probability of event *A* given *B* is 0.60.

23. Suppose an experiment has three mutually-exclusive events, *A*, *B*, and *C*, with *p(A)* = 0.34, *p(B)* = 0.33, and *p(C) *= 0.33.

24. Suppose we have two events* A* and *B* with *p(A)* = 0.40 and *p(B)* = 0.20. Moreover, *p(A|B)* = *p(A)* and *p(B|A) = p(B).*

25. The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons: in 22 families, both father and the son attended college; in 31 families, neither father nor son attended college; in 12 families, the father attended college while the son did not; and in 35 families, the son attended college but the father did not.

26. We have the following probabilities and events: the prior probabilities for 2 events *E1* and *E2* are *p(E1) *= 0.50 and *p(E2)* = 0.50 and the conditional probilities are *p(E3|E1)* = 0.15 and *p(E3|E2)* = 0.70. Summarize this information in a table, and answer the 3 questions below.

28. We have the following probabilities and events: the prior probabilities for 3 events *E _{1}, E_{2},* and

*E*are

_{3}*p(E*= 0.10, and

_{1}) = 0.50, p(E_{2})*p(E*= 0.40 and the conditional probabilities are

_{3})*p(E*= 0:15,

_{4}|E_{1})*p(E*= 0.45 and

_{4}|E_{2})*p*(

*E*) = 0.70. Summarize this information in a table, and answer the 3 questions below.

_{4}|E_{3}