Extra Problems From Ch. 3
1) Do Problem 3.4 on p. 103 of Ross, for the case of i = 10 (and do only this portion of the problem).
Provide some justification for your answer (but no need for a
lengthy justification).
2) Do Problem 3.5 on p. 103 of Ross, but change the initial holdings of the urn to be 9 white balls and 6 black balls.
Show work to justify your answer.
3) Do part (a) of Problem 3.67 on p. 109 of Ross (i.e., give the conditional probability that both shots hit the duck given that
the duck is hit), making an assumption of independence in the obvious way. Express your answer in terms of
p1 and
p2. No need to
provide justification or show any work for this one.
(As a way to check your answer, I'll give you that if
p1 = 1, then the desired conditional probability is
p2, and if
p1 = 0, then the desired conditional probability is 0.)
4) Do part (a) of Problem 3.15 on p. 104 of Ross except make the initial contents of the urn 4 white balls and 6 black balls
instead of 5 white balls and 7 black balls.
Show adequate work
to justify your answer (which should be given as a number (and not left in terms of factorials, binomial coefficients, etc.)).
5) Do part (a) of Problem 3.21 on p. 104 of Ross except use 6 (instead of 5) for the percentage of students majoring in computer science.
Provide some justification for your answer.
6) Do Problem 3.31 on p. 105 of Ross, except for the second drawing, make it only one ball and obtain the probability that is has
never been used. (So we start with 9 new and 6 used balls and randomly draw (without replacement) 3 of them. After they are
used and put back in the box, the box would then contain anywhere from 6 to 9 balls which have never been used. Give the probaility
that if a single ball is drawn from the box after the three have been replaced, the single ball drawn will not have been previosuly used.)
Show adequate work
to justify your answer (which should be given as a number (and not left in terms of factorials, binomial coefficients, etc.)).
7) Do Problem 3.40 on p. 106 of Ross, except
make the contents of Urn A 4 white balls and 8 black balls
instead of 5 white balls and 7 black balls.
Show adequate work
to justify your answer.