Download Sec. 3.3 – The Addition Rule

Sec. 3.3 – The Addition Rule
Two events A and B are ________________ _______________ if A and B cannot
occur at the same time.
Decide whether or not the events are mutually exclusive.
Event A: Roll a 3 on a die.
Event B: Roll a 4 on a die.
Event A: Randomly select a male student.
Event B: Randomly select a nursing major.
Event A: Randomly select a blood donor with type O blood.
Event B: Randomly select a female blood donor.
The Addition Rule
The probability that events A or B will occur, 𝑃(𝐴 𝑜𝑟 𝐵), is given by
__________________________________
If events A and B are mutually exclusive the rule can be simplified to
__________________________________
Find the probabilities of the following events.
You select a card from a standard deck.
a. Find the probability that the card is a 4 or an ace.
b. Find the probability that the card is a diamond or a 7.
c. Find the probability that the card is a red suit or a queen.
d. Find the probability that the card is a 3 or a face card.
You roll a six-sided die.
a. Find the probability of rolling a number less than three or rolling an odd
number.
b. Find the probability of rolling a 6 or a number greater than 4.
c. Find the probability of rolling a number less than 5 or an odd number.
d. Find the probability of rolling a 3 or an even number.
A college has an undergraduate enrollment of 3500. Of these 860 are business
majors and 1800 are women. Of the business majors, 425 are women. If a college
newspaper conducts a poll and selects students at random to answer a survey,
find the probability that a selected student is a woman or a business major.
The table shows the results of a survey that asked 3203 people whether they
wear contacts or glasses. A person is selected at random from the sample. Find
the probability of each event.
Male
Female
Total
Contacts
Only
64
189
253
Glasses
Only
841
427
1268
Both Glasses
and Contacts
177
368
545
Neither
456
681
1137
a. The person wears contacts only or glasses only.
b. The person is male or wears both contacts and glasses.
c. The person is female or wears neither contacts nor glasses.
d. The person is male or does not wear glasses.
Total
1538
1665
3203
Type of Probability and
probability rules
In words
The number of outcomes in the
sample space is known and each
outcome is equally likely to occur.
The frequency of outcomes in the
sample space is estimated from
experimentation.
The probability of an event is between
0 and 1, inclusive.
The complement of event E is the set
of all outcomes in a sample space that
are not included in 𝐸, denoted by 𝐸′.
The Multiplication Rule is used to find
the probability of two events occurring
in a sequence.
The Addition Rule is used to find the
probability of at least one of two
events occurring.
In symbols