Question

A jar contains 6 marbles numbered 1 through 6. An experiment consists of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card (hearts, diamonds, clubs, or spades).

How many outcomes are in the sample space for this experiment?

Answer 1

24 Outcomes

Explanation:

The sample space of an event is the set of all possible outcomes.

A jar contains 6 marbles numbered 1 through 6

Sample Space of Selecting a Marble from the Jar =6

A standard deck contains 4 Suits

Sample Space of Selecting a Card and Observing the Suit = 4

Theorem(The Fundamental Counting Principle)

If there are “x” ways for one event to happen, and “y” ways for a second event to happen, then there are “x * y” ways for both events to happen.

Therefore the Sample Space of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card is given as:

Sample Space of Selecting a Marble X Sample Space of Selecting a Card and observing the Suits

= 6 X 4

=24

There are 24 Outcomes in this experiment.