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# Simple Probability

Simple probability refers to the likelihood or chance of an event occurring, often expressed as a ratio of the number of favorable outcomes to the total number of possible outcomes.

It is used to quantify uncertainty and make predictions based on given information.

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## Formula

The formula for simple probability P(A) of event A occurring is:

P(A) = Number of favorable outcomes/Total number of possible outcomes

## Explanation

To find the simple probability of an event, we count the number of favorable outcomes (outcomes where the event occurs) and divide it by the total number of possible outcomes.

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## Example Questions

1. What is the probability of rolling a 4 on a fair six-sided die?

Solution

Number of favorable outcomes: 1 (rolling a 4)

Total number of possible outcomes: 6 (since there are six sides on the die)

P(rolling a 4) = 1/6

So, the probability of rolling a 4 on a fair six-sided die is 1/6

2. A bag contains 4 red balls, 3 blue balls, and 2 green balls. What is the probability of randomly selecting a blue ball from the bag?

Solution

Number of favorable outcomes: 3 (selecting a blue ball)

Total number of possible outcomes: 9 (since there are 9 balls in total)

P(selecting a blue ball) = 3/9 = 1/3

So, the probability of randomly selecting a blue ball from the bag is 1/3

3. A jar contains 10 marbles, of which 6 are red and 4 are blue. If one marble is drawn at random from the jar, what is the probability that it is not blue?

Solution

Number of favorable outcomes: 6 (selecting a red marble)

Total number of possible outcomes: 10 (since there are 10 marbles in total)

P(not blue) = 6/10 = 3/5

So, the probability of drawing a marble that is not blue is ⅗

## Simple Probability FAQS

#### What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility (the event will never occur) and 1 indicates certainty (the event will always occur).

#### How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The formula for probability P of an Event E is:

P(E) = Total number of favorable outcomes/Total number of possible outcomes

#### What is the difference between experimental and theoretical probability?

Experimental probability is based on observed outcomes from experiments or trials, while theoretical probability is calculated based on mathematical principles and assumptions.

#### What is the probability of an event not occurring?

The probability of an event not occurring is equal to 1 minus the probability of the event occurring:

P(not E) = 1 – P(E)

#### What is the probability of mutually exclusive events?

Mutually exclusive events are events that cannot occur at the same time. The probability of mutually exclusive events A and B occurring is the sum of their individual probabilities:

P(A U B) = P(A) + P(B)

#### What is the probability of independent events?

Independent events are events where the outcome of one event does not affect the outcome of the other. The probability of independent events A and B occurring is the product of their individual probabilities:

P(A ∩ B) = P(A) x P(B)

#### What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It is calculated using the formula:

P(A|B) = P(A ∩ B)/P(B)

#### What is the probability of complementary events?

Complementary events are events that are mutually exclusive and together cover all possible outcomes. The probability of one event occurring is equal to 1 minus the probability of the complementary event occurring:

P(E) + P(not E) = 1

#### How do you calculate the probability of multiple events?

To calculate the probability of multiple events occurring, multiply the probabilities of each individual event together if they are independent, or use conditional probability if they are dependent.

#### What are some real-life applications of probability?

Probability is used in various real-life scenarios such as weather forecasting, risk assessment in insurance, predicting stock market trends, making decisions in games of chance, and analyzing results in scientific experiments.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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