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
