Extra Problems From Ch. 3 and Ch. 4
1) Do part (d) of Problem 3.59 on p. 108 of Ross, assuming that the woman is randomly selected from all women alive on earth..
Answer yes or no and provide simple justification for your answer.
2) Do part (a) of Problem 3.80 on pp. 110 of Ross, giving the value of the desired probability, along with a very simple (perhaps just one or
two words) explanation for your answer. (Note: I'm looking for one specific word in your explanation/justification.
If you're puzzled, and can't determine what that word is,
try to give some sort of reasonable justification. (Hint: Try to come up with the
desired probability
without writing any work down. Then determine how you can justify your probability.))
3) Consider Theoretical Exercise 3.2 on p. 113 of Ross, and express P(B|A) as simply as possible.
(As an example of what Ross means, for the first part, P(A|B), we can note that
since A is a subset of B, the intersection of
A and B is just
A, so that for
P(A|B), instead of writing
P(AB)/P(B), we can just write
P(A)/P(B).)
4) Do part (a) of Problem 4.7 on p. 175 of Ross, being sure to note that just the possible values and not also their probabilities
are requested.
5) Do Problem 4.14 on p. 176 of Ross, assuming the five players get one number each.
Show adequate work to clearly justify your answer. (Hint: Perhaps it will be good to start by obtaining value for
P(X >= i) (i = 0, 1, 2, 3, 4), and then obtain the desired values of
P(X = i) (i = 0, 1, 2, 3, 4) by subtraction. To get
P(X >= i), think about how player 1's number must compare to the numbers of players 2 through i, and use
a symmetry argument.)