Transcript Lesson 4

Lesson 14-4
Probability Distributions
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Objectives
• Use random variables to compute probability
• Use probability distributions to solve realworld problems
Vocabulary
• Random variable –
• Probability distribution –
• Probability histogram –
Laws of Probabilities
1. The probability of an event must be between 0 and 1
2. Sum of all events’ probability must be equal to 1
3. A probability of an event that is equal to zero is an
event that is impossible
4. A probability of an event that is equal to one is an
event that is a certainty
Example 1a
The owner of a pet store asked
customers how many pets they
owned. The results of this
survey are shown in the table.
A. Find the probability that a
randomly chosen customer
has at most 2 pets.
Number
of Pets
0
Number of
Customers
3
1
37
2
3
4
33
18
9
There are 3 + 37 + 33 or 73 outcomes in which a customer
owns at most 2 pets, and there are 100 survey results.
Answer: The probability that a randomly chosen
customer owns at most 2 pets is
Example 1b
The owner of a pet store asked
customers how many pets they
owned. The results of this
survey are shown in the table.
Number
of Pets
0
Number of
Customers
3
1
37
2
3
4
33
18
9
B. Find the probability that a
randomly chosen customer
has 2 or 3 pets.
There are 33 + 18 or 51 outcomes in which a customer owns 2
or 3 pets.
Answer: The probability that a randomly chosen
customer owns 2 or 3 pets is
Example 2a
The table shows the probability
distribution of the number of
students in each grade at
Sunnybrook High School.
A. If a student is chosen at
random, what is the probability
that he or she is in grade 11 or above?
X = Grade
9
10
11
12
P(X)
0.29
0.26
0.25
0.2
Recall that the probability of a compound event is the sum of the
probabilities of each individual event.
The probability of a student being in grade 11 or above is the sum
of the probability of grade 11 and the probability of grade 12.
Sum of individual P(X)
Answer: The probability of a student in grade 11 or above is 0.45.
Example 2b
B. Make a probability
histogram of the data.
Draw and label the vertical and
horizontal axes. Remember to use
equal intervals on each axis. Include a
title.
Answer:
X = Grade
9
10
P(X)
0.29
0.26
11
12
0.25
0.2
Summary & Homework
• Summary:
– Probability distributions have the following
properties:
• For each value of X, 0 ≤ P(X) ≤ 1
• The sum of probabilities of each value of X is 1 (∑P(Xi) = 1)
• Homework:
– none