Download Chapter 12 Probability and Statistics

Chapter 12 Probability and Statistics
Review
12.4 Probability of Compound Events
The school council comprises 3 male students, 5 female students, and 2 teachers.
1. What is the probability that a person chosen at random from the school council is a
female student?
2. What is the probability that both members of a committee chosen at random from the
school council are male students?
Compound Events:
Union: either in A or in B
Intersection: in both A and B
If the intersection is empty, Mutually Exclusive Events and P(A or B)=P(A) +P(B)
If intersection is not empty, then adding them “double counts” the middle so…
P(A or B) = P(A) + P(B) – P(A and B)
Ex)
P(A) = 0.6
P(B) = 0.2
P(A or B) = ?
P(A and B) = 0.1
Mutually Exclusive?
Ex)
P(A) = 30%
P(B) = ?
P(A or B) = 10%
P(A and B) = 50%
Mutually Exclusive?
Example 1)
A card is randomly selected from a standard deck of 52 cards. What is the probability
that it is an ace or a face card?
Example 2)
One six-sided die is rolled. What is the probability of rolling a multiple of 3 or 5?
Example 3)
A card is randomly selected from a standard deck of 52 cards. What is the probability
that the card is a heart or a face card?
Example 4)
One six-sided die is rolled. What is the probability of rolling a multiple of 3 or a multiple
of 2?
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Example 5)
In a poll of high school juniors, 6 out of 15 took a French class and 11 out of 15 took a
math class. Fourteen out of 15 students took French or math. What is the probability that a
student took both French and math?
The event A’, called the complement of event A, consists of all outcomes that are not in A. The
notation A’ is read “A prime”
P A'  1  P A
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Example 6)
When two six-sided dice are tossed, there are 36 possible outcomes (pg. 726). Find the
probability of the given event.
a.) the sum is not 8
b.) the sum is greater than or equal to 4
Example 7)
A card is randomly selected from a standard deck of 52 cards. Find the probability of
the given event.
a.) the card is not a king
b.) the card is not an ace or a jack
H-Example 8)
One high school requires students to complete 30 hours of community service to
graduate. There are 156 different community service options to choose from. What is the
probability that in a group of 5 students, at least 2 of them will be doing the same community
service?
Puzzler
In one community, it is never sunny and rainy at the same time. The probability of rain is 3
times the probability of sun and the probability that it rains or is sunny is .88. What is the
probability that it will rain in this community?
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