Chapter 15: In Class Group Practice
1. Suppose that in a certain town, 60% have an auto insurance policy with State Farm, 40%
have a homeowner’s policy with State Farm, and 25% have both. Define A = has an auto
insurance policy and H = has homeowner’s insurance. Find the following, and explain what
each represents.
(
)
(a) P A and H C
(
(b) P AC and H C
(c) P ( A H )
)
(
(d) P H AC
)
2. Suppose that 68% of all people have ham for Christmas dinner, 39% have turkey, and 10%
have roast beast (you know, like in Whoville). Suppose further that 16% have both ham and
turkey, 5% have both turkey and roast beast, 7% have ham and roast beast, and 3% have all
three. Define T = has turkey, H = has ham, R = has roast beast. Find the following, and
explain what each represents.
(
)
(e) P (T R)
(
)
(f) P (T and H ) RC
(a) P H C and T
(b) P H and RC
(
(c) P H C and T C and RC
(
)
(d) P ( H T )
)
(
)
( (
))
(g) P ( R and H ) T
(h) P H R and T C
3. For a certain disease, the probability that a person has this disease is 0.001. A test that
checks for this disease is accurate 95% of the time. A person is randomly selected. Find the
following probabilities.
(a) P(person tests negative for this disease)
(b) P(has the disease and tests negative for it)
(c) P(tests negative for the disease given that (s)he has the disease)
(d) P(has the disease given that (s)he tests positive for the disease)
4. In a certain town, 49.1% are male while 50.9% are female. Of the males, 22.9% admit to
having gambled on High School Athletics whereas only 4.5% of the females admit to having
done so. Suppose a teenager from this town is randomly selected. Find the following
probabilities.
(a) P(person has gambled on high school athletics)
(b) P(person is female and has gambled on high school athletics )
(c) P(person is male given that he has gambled on high school athletics)
(d) P(person is a female given that she has gambled on high school athletics)
Answers
1.
(a)
(b)
(c)
(d)
0.35; has auto insurance but not homeowner’s insurance with State Farm
0.25; has neither auto nor homeowner’s insurance with State Farm
0.625; has auto policy given (s)he has homeowner’s insurance with State Farm
0.375; has homeowner’s insurance given (s)he does not have an auto policy with State Farm
2.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
0.23; has turkey but not ham
0.61; has ham but not roast beast
0.08; does not have ham, turkey, or roast beast
0.4103; has ham given they have turkey
0.50; has turkey given they have roast beast
0.1444; has turkey and ham given they do not have roast beast
0.0769; has roast beast and ham given they have turkey
0.80; has ham given that they have roast beast but not turkey
3.
(a)
(b)
(c)
(d)
0.9491
0.00005
0.05
0.0187
4.
(a)
(b)
(c)
(d)
0.135344
0.022905
0.8308
0.1692