Download Set Prob 7 - Non-Mutually Exclusive

Math 30-2
Set Theory & Probability: Lesson #7
Probability of Non-Mutually Exclusive Events
Objective: By the end of this lesson, you should be able to:
- use Venn diagrams to represent non-mutually exclusive events
- solve a contextual problem that involves the probability of non-mutually exclusive events
All the problems we looked at last class involved the probability of mutually exclusive (or
disjoint) events. Today we will look at how these problems change if the events are not mutually
exclusive.

Non-mutually exclusive events –
Let’s compare the Venn diagram of mutually exclusive events to the Venn diagram of nonmutually exclusive events.
Mutually Exclusive
Non-Mutually Exclusive
Because of the overlapping region, the formula for the probability of one or the other of nonmutually exclusive events is like the Principle of Inclusion and Exclusion.
e.g. 1) Reid’s mother buys a new washer and dryer set and is trying to decide whether to buy the
3-year extended warranty for $450. Reid does some research on the repair statistics for
this particular brand of washer and dryer and summarizes the findings in the table below:
Probability of needing
Average
Appliance
repairs within 3 years
repair cost
Washer
0.22
$400
Dryer
0.13
$300
Both
0.03
$700
a) What is the probability that Reid’s mother will need to get repairs to her new washer
or dryer within three years?
Math 30-2
Set Theory & Probability: Lesson #7
b) Do you think she should buy the extended warranty? Why or why not?
e.g. 2) According the weather forecast, there is a 35% chance of snow tomorrow and a 65%
chance of snow the next day.
a) Carly says that since 35% + 65% = 100%, it means that it is certain to snow within
the next two days. Is she correct? Explain.
b) If the probability that it will snow both days is 22%, what is the probability that it will
snow within the next two days?
c) What are the odds against snow in the next two days?
e.g. 3) A school newspaper published the results of a recent survey:
a) Are skipping breakfast and skipping lunch mutually
exclusive events? Explain.
b) Draw a Venn diagram of the situation.
Eating Habits: Student
Survey Results
58% skip breakfast
22% skip lunch
29% eat both breakfast and
lunch
c) Determine the probability that a randomly selected student skips both breakfast and
lunch.
Math 30-2
Set Theory & Probability: Lesson #7
d) Explain three different ways to determine the probability that a randomly selected
student skips at least one of breakfast or lunch.
e.g. 4) James is playing poker. He has the cards 6♣, 7♣, 8♣, 9♣, and needs to draw one more
card. His opponent has three of a kind.
James will win the hand if he can get a hand better than three of a kind. (For poker hand
rankings, see: http://www.pokerlistings.com/poker-hand-ranking.) If James draws a 5 or
a 10 of clubs, he will have a straight flush. If he draws any other club, he will have a
flush. If he draws any other 5 or 10, he will have a straight.
Determine the probability that James will beat his opponent. (Hint: Remember that there
are already four cards in his hand, and he cannot draw those cards again!)
Assignment:
p. 176-180 #2-3, 7b, 8-9, 12-16
For a challenge: #19