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1) Researchers are interested in the relationship between cigarette smoking and
lung cancer. Suppose an adult male is randomly selected from a particular
population. Assume that the following table shows some probabilities
involving the compound event that the individual does or does not smoke and
the person is or is not diagnosed with cancer.
Event
Probability
Smokes and gets cancer
.05
Smokes and does not get cancer .20
Does not smoke and gets cancer .03
Does not smoke and does not get cancer
.72
Suppose further that the probability that the randomly selected individual is a
smoker is .25.
a) Find the probability that the individual gets cancer, given that he is a smoker.
b) Find the probability that the individual does not get cancer, given that he is a
smoker.
c) Find the probability that the individual gets cancer, given that he does not
smoke.
d) Find the probability that the individual does not get cancer, given that he does
not smoke.
2) The probability that a car will skid on a bridge on
a rainy day is .75. Today the weather station
announced that there is a 20% chance of rain.
What is the probability that it will rain today and
that a car will skid on the bridge?
3) The probability that Ted will enroll in an English
class in 1/3. If he does enroll in an English
class, the probability that he would enroll in a
math class is 1/5. What is the probability that
he enrolls in both classes?
5) The local Chamber of Commerce conducted a survey of one
thousand randomly selected shoppers at a mall. For all shoppers,
“gender of shopper” and “items shopping for” was recorded.
Items shopping for
Gender Clothing Shoes
Other
Total
Male
75
25
150
250
Female
350
230
170
750
Total
425
255
320
1000
a)
b)
c)
d)
e)
f)
What is the probability that the shopper is a female?
What is the probability that the shopper is shopping for shoes?
What is the probability that the shopper is a female shopping for
shoes?
What is the probability that the shopper is shopping for shoes
given that the shopper is a female?
Are the events “female” and “shopping for shoes” disjoint?
Are the events “female” and “shopping for shoes” independent?
6) Two companies offer overnight shipping
that is supposed to arrive by 10:00 a.m.
Your company ships 30% of its packages
with shipping service 1 and 70% with
shipping service 2. Shipping service 1 fails
to meet the 10:00 a.m. deadline 10% of
the time and shipping service 2 fails to
meet it 8% of the time. If a customer is
expecting a package and it is late, which
of the shipping services is the more likely
to have been used? (Hint: use a tree
diagram).