Math 362K Probability Fall 2007 Instructor: Geir Helleloid
Weekly Homework 6 Solutions
1. (Chapter 4, Problem 48) It is known that diskettes produced by a certain company
will be defective with probability .01, independently of each other. The company sells
the diskettes in packages of size 10 and offers a money-back guarantee that at most 1
of the 10 diskettes in the package will be defective. If someone buys 3 packages, what
is the probability that he or she will return exactly 1 of them?
Solution. The number of defective diskettes Xin a package is a Binomial(10, .01)
random variable. The probability that at most 1 of the diskettes in a package is
defective is
P(X≤1) = P(X= 0) + P(X= 1)
=10
0×(.99)10 +10
1×(.01)1×(.99)9
≈.9957
The number of packages Yreturned by the customer is itself a Binomial(3, 0.0043
) random variable, since she returns each of the three packages independently with
probability 1-0.9957. So the probability that the customer returns exactly 1 of the 3
packages is
P(Y= 1) = 3
1×(1 −0.9957) ×.99572=.0127 .
2. (Chapter 4, Problem 49a) When coin 1 is flipped, it lands heads with probability .4;
when coin 2 is flipped, it lands heads with probability .7. One of these coins is randomly
chosen and flipped 10 times. What is the probability that exactly 7 of the 10 flips land
on heads?
Solution. The number of heads Xobtained when flipping coin 1 ten times is a Bino-
mial(10, .4) random variable. The number of heads Yobtained when flipping coin 2
ten times is a Binomial(10, .7) random variable. The probability that coin 1 lands
heads up exactly 7 times is
P(X= 7) = 10
7×(.4)7×(.6)3≈.0425
The probability that coin 2 lands heads up exactly 7 times is
P(Y= 7) = 10
7×(.7)7×(.3)3≈.2668
