Question

Consider an experiment where we ask what type of car – either domestic (e.g., Chevrolet, Ford, Chrysler, etc.), foreign built abroad (e.g. a Toyota built in Japan) or foreign built in the U.S. (e.g., a Toyota built in Kentucky) – and the style (sedan, hatchback, truck or SUV) of the automobiles driven by 20 different people. How many outcomes are in the sample space?

Answer 1

`12^(20)` outcomes for this sample space (under some considerations)

Explanation:

Let's define the multiplication principle.

If a first part of an experiment can happen in n1 ways, a second part of an experiment can happen in n2 ways , . . . , a i - part of an experiment can happen in ni ways, then the total outcomes for the all the experiment are

(n1) x (n2) x ... x (ni)

In this exercise n1 = domestic

n1 is the total classes for domestic category

(Let's suppose n1 = 3 because of Chevrolet, Ford and Chrysler)

n2 = 1 (Also supposing we only have ''a Toyota built in Japan'' category for n2)

n3 = 1 (Also supposing we only have ''A Toyota built in Kentucky'' category for n3)

n4 = 4 (Also supposing we only have ''sedan,hatchback, truck or SUV'' category for n4

The possible outcomes for one person in the experiment are

`(Domestic).(ForeignBuiltAbrod).(ForeignBuiltInTheU.S).(Style)`

Where what it is brackets are the possible categories for that classification.

`n1.n2.n3.n4=3.1.1.4=12`

We have 20 different people then
`12^(20)` are the possible outcomes sample space

In the sample space there are
`12^(20)` outcomes if we consider that we have 3 types of domestic car, 1 type of foreign car built abroad,1 type of foreign car built in the U.S and 4 differents styles for this 20 different people.