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Author:
Al Greene

To identify the theoretical probability of an event.

To identify the odds of an event.

This packet talks about probability, both theoretical and experimental, and odds. There are definitions, examples, and problems for you to test your understanding.

Tutorial

This packet discusses the concepts of probability and odds. These terms are defined, and applied to simple situations to illustrate the ideas.

Source: Greene

This video gives a dice example and finds the odds for, odds against, and probability of getting a 3.

Source: YouTube

This sections will test your understanding of probability and odds.

1. What is the probability of getting an even number on a roll of a fair dice?

2. What are the odds for getting a spade on one draw from a standard deck?

3. What are the odds against getting a tails on a flip of a fair coin?

Suppose we have a parking lot that has 10 total cars: 3 blue, 5 red, and 2 green.

What is the probability of, odds for, and odds against one randomly selected car being blue?

Source: Greene

1. What is the probability of getting an even number on a roll of a fair dice? There are three even numbers on a die (2,4, and 6), and there are 6 total numbers. So our probability is 3/6, or 1/2, or .5.

2. What are the odds for getting a spade on one draw from a standard deck? There are 13 spades in a deck, as there are with every suit. Since there are three other suits, that means there are 13x3 = 39 cards that are not spades. Therefore, the odds for getting a spade on one draw from a deck are 13:39, or 1:3. This can also be expressed as 1 to 3, or 1/3.

3. What are the odds against getting a tails on a flip of a fair coin? There are two outcomes when you flip a coin, a heads or a tails. So there is one way to get a tails, and one way to not get a tails (heads). Thus, the odds against getting a tails are 1:1, or 1 to 1, or 1/1.

Suppose we have a parking lot that has 10 total cars: 3 blue, 5 red, and 2 green.

What is the probability of, odds for, and odds against one randomly selected car being blue?

Probability: We have 3 blue cars, and 10 total cars. Therefore, the probability of a randomly selected car being blue is 3/10.

Odds for: We have 3 blue cars, and 7 cars that are not blue (5 red, 2 green). So the odds for getting a blue car is 3:7.

Odds against: This will just be the opposite of the odds for. There are 7 cars that aren't blue, and 3 cars that are. SO the odds against getting a blue car are 7:3.

Source: Greene