What is Probability?

Probability is the measure of the likelihood that an event will occur. It ranges from 0 (impossible event) to 1 (certain event). Probability helps in assessing risk and making predictions.

Basic Probability Concepts

• Experiment: A procedure that produces outcomes. For example, rolling a dice.

• Outcome: A possible result of an experiment. For example, getting a 4 when rolling a dice.

• Event: A set of outcomes of an experiment. For example, rolling an even number.

• Sample Space:The set of all possible outcomes of an experiment. For example, the sample space for rolling a dice is {1, 2, 3, 4, 5, 6}.

Probability Rules

• Addition Rule: The probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. For example, the probability of rolling a 2 or a 4 on a dice is 1/6 + 1/6 = 1/3.

• Multiplication Rule: The probability of two independent events both occurring is the product of their individual probabilities. For example, the probability of flipping a coin and getting heads twice is 1/2 * 1/2 = 1/4.

Probability Distributions

• Uniform Distribution: All outcomes are equally likely. For example, rolling a fair dice.

• Normal Distribution: Data is symmetrically distributed with a bell-shaped curve. Many natural phenomena follow a normal distribution, such as heights or test scores.

Example

The probability of rolling a 3 on a fair six-sided dice is 1/6. The probability of rolling either a 3 or a 5 is 1/6 + 1/6 = 1/3. The probability of flipping a coin and getting heads is 1/2.

Activity

Calculate the probability of drawing an Ace from a standard deck of 52 cards. What is the probability of drawing an Ace or a King? What is the probability of drawing an Ace and then a King without replacement?

Quiz