Sample Space

Front

What is a sample space in probability?

Back

The sample space is the set of all possible outcomes of a random experiment.

Front

How many outcomes are there when rolling two six-sided dice?

Back

There are 36 possible outcomes when rolling two dice (6 sides on the first die multiplied by 6 sides on the second die).

Front

What is the sample space for a spinner that has the sections: 1, 1, 1, 1, 2, 3, 4, 4?

Back

The sample space is {1, 1, 1, 1, 2, 3, 4, 4}, which includes the outcomes represented by the sections of the spinner.

Front

How do you calculate the total number of outcomes when tossing a coin and rolling a die?

Back

You multiply the number of outcomes for the coin (2) by the number of outcomes for the die (6), resulting in 12 total outcomes.

Front

If a car model comes in 4 trim levels, 5 colors, and 3 interiors, how do you find the total number of different versions?

Back

Multiply the number of options: 4 trim levels x 5 colors x 3 interiors = 60 different versions.

Front

What is the principle of counting in probability?

Back

The principle of counting states that if one event can occur in 'm' ways and a second can occur independently in 'n' ways, then the two events can occur in m*n ways.

Front

What is a tree diagram and how is it used in probability?

Back

A tree diagram is a visual representation of all possible outcomes of a sequence of events, used to calculate probabilities.

Front

What is the difference between a discrete and continuous sample space?

Back

A discrete sample space consists of distinct, separate outcomes, while a continuous sample space includes an infinite number of possible outcomes within a range.

Front

How do you determine the sample space for a single die roll?

Back

The sample space for a single die roll is {1, 2, 3, 4, 5, 6}.

Front

What is the formula for calculating combinations?

Back

The formula for combinations is C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of items, and 'k' is the number of items to choose.