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Unit 3Lesson 3 3 min read

Basic Probability and Odds

15/18

Learning Objectives

Define probability and the range of possible probabilities (0 to 1).
Calculate the probability of a simple event and the probability of its complement.
Distinguish between probability and odds.
Calculate the odds in favor of a simple event.

The Math of Chance

How likely is something to happen? Probability is a branch of mathematics that gives us a way to measure the chance or likelihood of an event. It's a powerful tool for making predictions and understanding situations involving uncertainty.

Simple Probability

The probability of a single event happening is a ratio of the number of ways that event can occur to the total number of possible outcomes.

Probability(Event) = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)

Probability is always a number between 0 and 1.

A probability of 0 means the event is impossible.
A probability of 1 means the event is certain.

Example: What is the probability of drawing a Queen from a standard 52-card deck?

Number of Favorable Outcomes: There are 4 Queens in a deck.
Total Number of Possible Outcomes: There are 52 cards in total.
P(Queen) = 4 / 52
This fraction simplifies to 1/13.

Complement of an Event

The complement of an event is the chance that the event does not happen. The probability of an event and the probability of its complement always add up to 1.

P(Event does not happen) = 1 - P(Event happens)

Example: What is the probability of not drawing a Queen?

P(not Queen) = 1 - P(Queen)
P(not Queen) = 1 - (1/13) = 12/13
This makes sense, as there are 48 cards that are not Queens (48/52 = 12/13).

Probability vs. Odds

Probability and odds are related, but they are not the same thing. They are two different ways of expressing the likelihood of an event.

Probability compares the number of favorable outcomes to the total number of outcomes.
Odds compares the number of favorable outcomes to the number of unfavorable outcomes.

Odds in Favor(Event) = (Number of Favorable Outcomes) : (Number of Unfavorable Outcomes)

Example: Let's find the probability and odds of rolling a 2 on a standard six-sided die.

Favorable outcomes = 1 (rolling a '2')
Total outcomes = 6 (1, 2, 3, 4, 5, 6)
Unfavorable outcomes = 5 (rolling a 1, 3, 4, 5, or 6)
Probability of rolling a 2:
Favorable / Total = 1/6
Odds in favor of rolling a 2:
Favorable : Unfavorable = 1:5 (read as '1 to 5')

Odds are commonly used in sports betting and games of chance.

Key Terms

**Probability
The likelihood of an event occurring, expressed as a ratio of favorable outcomes to total possible outcomes. It is a number between 0 and 1.
**Favorable Outcome
The specific outcome or result that one is interested in.
**Total Outcomes
The complete set of all possible results of an experiment.
**Complement (of an event)
All outcomes that are NOT the event of interest. The probability of an event and its complement sum to 1.
**Odds
A ratio that compares the number of favorable outcomes to the number of unfavorable outcomes.

Check Your Understanding

1

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

2

The probability of rain tomorrow is 40%. What is the probability that it will not rain?

3

What are the odds in favor of rolling an even number on a standard six-sided die?