IXL - Write a discrete probability distribution (Precalculus practice)

At their family reunion, the McCarthy family recorded everyone's age.

Age	Number of people
49	2
71	4
78	2
97	2

is the age of a randomly chosen person. Write the probability distribution of

in the table below.

Write each probability as a decimal.

X	P ( X )
49	0.2
71
78	0.2
97	0.2

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Learn with an example

question

An architecture student measured the heights of all the buildings downtown.

Height (meters)	Number of buildings
10	4
46	3
63	3

is the height of a randomly chosen building. Write the probability distribution of

in the table below.

Write each probability as a decimal.

X	P ( X )
10	0.4
46	0.3
63

key idea

A random variable is a function that assigns a numerical value to each outcome in a sample space. Note that though random variables are functions, they are usually denoted by letters like

is a random variable,

(

)

(

)

is the probability that

takes the value

The function that maps

(

)

is the probability distribution of

A probability distribution is frequently represented as an equation, table, or graph.

A uniform probability model is a sample space in which all outcomes are equally likely.

In a uniform probability model, the probability of an event

is the number of outcomes in that event divided by the total number of outcomes in the sample space:

(

)

# of outcomes in

total # of outcomes

solution

Each building is equally likely to be chosen. So, to find the probability that a building of a particular height is chosen, divide the frequency of that height by the total number of buildings.

Count the total number of buildings.

Add the frequencies of each height to find the total number of buildings:

Write the probability distribution of

Divide each frequency by 10 to find the probability that a building chosen at random is a particular height.

X	P ( X )
10	0.4
46	0.3
63	0.3

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