Probability is the likelihood of a specific outcome or event occurring, expressed as a number between 0 and 1. A probability of 0 means the event will not occur, and a probability of 1 means the event is certain to occur.

**Sample Space:**The set of all possible outcomes of an experiment. It is denoted by S.**Event:**A subset of the sample space, representing a specific outcome or a set of outcomes.**Probability of an Event:**The likelihood of an event occurring, denoted by P(E), where E is the event.

The probability of an event E is calculated using the formula:

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

**Classical Probability:**Based on equally likely outcomes. P(E) = Number of favorable outcomes / Total number of possible outcomes.**Experimental Probability:**Based on observed data from experiments or real-life situations. P(E) = Number of times event occurs / Total number of trials.**Subjective Probability:**Based on personal judgment or experience.

**Addition Rule:**P(A or B) = P(A) + P(B) - P(A and B), where A and B are events.**Multiplication Rule:**P(A and B) = P(A) * P(B|A), where A and B are events, and P(B|A) is the probability of B given that A has occurred.**Complement Rule:**P(not A) = 1 - P(A), where A is an event.

1. A fair six-sided die is rolled. What is the probability of rolling a 3?

P(rolling a 3) = 1/6

2. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble?

P(drawing a blue marble) = 3/10

3. In a game, a player wins with a probability of 0.3. What is the probability of the player losing?

P(losing) = 1 - 0.3 = 0.7

4. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart or a spade?

P(heart or spade) = P(heart) + P(spade) - P(heart and spade) = 13/52 + 13/52 - 0 = 26/52 = 1/2

5. Two coins are flipped. What is the probability of getting exactly one head?

P(exactly one head) = P(H1, T2) + P(T1, H2) = 1/4 + 1/4 = 1/2

Probability is a fundamental concept in mathematics and has applications in various real-life scenarios, such as games, statistics, and decision-making. Understanding probability allows us to make informed predictions and analyze uncertain outcomes.

Study GuideProbability Worksheet/Answer key

Probability Worksheet/Answer key

Probability Worksheet/Answer key

Probability Worksheet/Answer key

Probability Concepts

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Data Analysis and Probability (NCTM)

Understand and apply basic concepts of probability.

Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.

Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.