Theoretical Probability, Sample Space & Complementary Events

Front

What is theoretical probability?

Back

Theoretical probability is the likelihood of an event occurring based on all possible outcomes, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

How do you calculate the theoretical probability of rolling an even number on a six-sided die?

Back

The theoretical probability is calculated as the number of even outcomes (3: 2, 4, 6) divided by the total outcomes (6), which simplifies to 1/2.

Front

What is a sample space?

Back

A sample space is a list of all possible outcomes of an event.

Front

What is the sample space for rolling a standard six-sided die?

Back

The sample space is {1, 2, 3, 4, 5, 6}.

Front

What is the complement of an event?

Back

The complement of an event is the set of outcomes in the sample space that are not included in the event.

Front

If the probability of drawing a red marble is 0.5, what is the probability of not drawing a red marble?

Back

The probability of not drawing a red marble (the complement) is also 0.5.

Front

In a clothing store, if you can select shirts, pants, or jackets, what is the complement of selecting a jacket?

Back

The complement is not selecting a jacket, which includes selecting either a shirt or pants.

Front

What is the formula for calculating probability?

Back

Probability = (Number of favorable outcomes) / (Total number of possible outcomes).

Front

If a die is rolled, what is the probability of rolling a number greater than 4?

Back

The favorable outcomes are {5, 6}, so the probability is 2/6, which simplifies to 1/3.

Front

What does it mean if an event is certain?

Back

An event is certain if it has a probability of 1, meaning it will definitely occur.