Probability of a simple event step by step

What is a simple event?

A simple event is an outcome that cannot be broken down further. For example, flipping a coin results in either heads or tails.

Example of a simple event in a store?

Selecting a red shirt from a rack of shirts is a simple event.

What is the probability of an event?

The probability quantifies how likely an event is to occur, expressed as a number between 0 and 1.

True or false: Probability of an impossible event is 1.

False, because the probability of an impossible event is 0.

Difference between outcomes and sample space?

Outcomes are individual results of an experiment, while the sample space is the set of all possible outcomes.

Fill in the blank: Probability is calculated as __________.

the number of favorable outcomes divided by the total number of outcomes.

What is a favorable outcome?

A favorable outcome is an outcome that satisfies the conditions of the event we are interested in.

Scenario: Rolling a die. What’s the probability of rolling a 4?

There are 6 outcomes. The probability is $\displaystyle P(4) = \\frac{1}{6}$.

Which is NOT a characteristic of probability?

Probability must always be greater than 1. (This is false.)

What does it mean if the probability is 0.5?

It indicates an equal likelihood of the event occurring or not occurring.

Outcome when selecting a card from a standard deck?

The probability of drawing an Ace is $\displaystyle P(Ace) = \\frac{4}{52} = \\frac{1}{13}$.

True or false: All probabilities must add up to 1.

True, because the total probability of all possible outcomes equals 1.

How do we express the probability of a simple event?

Usually expressed as a fraction, decimal, or percentage.

Scenario: A jar with 3 red and 2 blue marbles. P(red)?

Total marbles = 5. $\displaystyle P(red) = \\frac{3}{5}$.

What is complementary probability?

The probability of the event not occurring, calculated as $\displaystyle P(A') = 1 - P(A)$.