AFM 113
Tutorial 4
Week 4
Question 1:
Canadian Blood services says that about 46% of the Canadian population have Type O blood,
42% have Type A blood, 9% have Type B blood, and the rest have Type AB. Among four
potential donors, what is the probability that
a)
All are Type O?
b)
No one is Type AB?
c)
At least one person is Type B?
d)
In the previous parts some of your answers depended on the assumption that the
outcomes described were disjoint. Other answers depended on the assumption that that
the events were independent. Do you understand the difference between disjoint and
independent?
i)
If you examine one person, are the events that the person is Type A and
that the Type B disjoint or independent or neither? Explain.
ii)
If you examine two people, are the events that the first is Type A and the
second is Type B disjoint or independent or neither? Explain.
iii)
Can disjoint events ever be independent? Explain.
Question 2:
Summit Projects provides marketing services and website management for many companies that
specialise in outdoor products and services. To understand customer Web behaviour, the
company experiments with different offers and website design. The results of such experiments
can help to maximise the probability that customers will purchase products during a visit to a
website. A recent experiment found that customers made purchases 6% of the time when offered
an instant discount, 5% of the time when offered free shipping, and 2% of the time when no
special offer was given. Suppose also that 20% of customers were offered the discount and an
additional 30% were offered free shipping.
a)
Set-up notation for this experiment and express the probabilities provided based on this
notation.
b)
Construct a tree diagram for this experiment
c)
What percentage of customers who visited the site made a purchase?
d)
Given that a customer made a purchase, what is the probability that the customer was
offered free shipping?
e)
Given that a customer made a purchase, what is the probability that the customer was
offered free shipping or a discount?
