Disjointed and Overlapping Event
Disjointed events (mutually exclusive) - are events that have no outcome in common
Overlapping events- events that have one or more outcomes in common
Tell if the events are disjointed or overlapping.
1.) Roll a number cube
Event A: roll a number less than 4
Event B: roll a 5
2.) Selecting a student
Event A: Select a 7th grader
Event B: Select a boy
Disjointed Events
P(A or B)= P(A) + P(B)
1.) What is the probability of rolling a number less than 4 or a number greater
than 4, when rolling a number cube?
2.) Fifty tickets are sold for a raffle. You buy 2 tickets, and your friend buys 3
tickets. One ticket is randomly chosen as the winner. What is the probability you
or your friend wins the raffle?
Overlapping Events
P(A or B)= P(A) + P(B) - P(A and B)
P(A or B) = the sum probabilities of the events minus the overlapping area
1.) What is the probability you will roll a number less than 5 or an even number?
# less than 5
even #
2.) You roll two number cubes. What is the probability that you roll a 4 on at least one of the
numbers?
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6
3,) At a college, 43% of the students are women, 15% of the students are art
majors, 4% have not chosen a major, and 8% are women and art majors. A faculty
member conducts an experiment and selects students at random to participate.
What is the probability that a randomly selected student will be either a woman or
an art major?
Complementary events: events that are disjointed and one event or the other must occur.
The sum of complementary events is 1.
1.) The forecast claims that there is a 40 percent chance of snow. What is the
probability that it will not snow?
Given P(A), find P(not A)
2. P(A) is 27% 3. P(A) =
Demonstrate Understanding
1.) Suppose you choose a book to read a random. Are the events " choosing a hard cover book"
and "choosing a fiction book" disjointed or overlapping? Explain.
2.) Give an example of overlapping events.
3.) In an election, candidate A received 35% of the votes, candidate B received 22% of the votes,
and candidate C received 43% of the votes. If you randomly select a person from all who voted,
what is the probability that the person selected voted for either candidate A or B?
4.) At a college, 51% of the students are women, 25% of the students are business majors, 5%
have not chosen a major, and 12% are women and business majors. A student newspaper
conducts a poll and selects students at random to answer a survey. What is the probability that a
randomly selected student will be either a
woman or a business major?
http://www.regentsprep.org/Regents/math/ALGEBRA/APR6/PracMut.htm