Common Probability Statements: Meaning & Application

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

If someone says the odds in favor of Justin winning the triathlon is one in ten, would you say that Justin will win for sure? Learn why this is not the case in this lesson along with other probability statements.

Odds For

You may think that the only place where probability comes into play is when you are gambling, but this is not the case. Probability comes into play when the weather man tells you what he thinks the weather will be today, tomorrow, and over the weekend. Probability also comes into play when talking about anything that might happen. For example, just by saying if you start studying now for your test in two weeks, you will most likely do better on the test than if you didn't, you are talking in probability. Probability is defined as the percentage likelihood that something will happen. It divides the number of times the specific event happens by the total number of all possible events. For example, if your friend is pregnant, then you can say that the probability that she will have a girl is 1 / 2 or 50 percent. The first number is when she has a girl and the second number is all possible events (she can have either a boy or a girl). Probability will always give you a number between 0 and 1 with 0 meaning the event will never happen and 1 meaning the event will always happen.

In this lesson, you'll learn about using the phrase odds for when talking about probability. This phrase has a slightly different meaning than that of probability. When you say odds, you are referring to the ratio of an event happening to the event not happening. For example, your pregnant friend has a 1:1 odds for getting a girl. She either gets a girl or a boy. Also, when referring to the lottery, you may see that your odds for winning is 1:1 million. You have 1 chance to win and 1 million chances to lose. When using the term odds for, your ratio will not always give you a number between 0 and 1 as you'll see.

Odds in Favor of

When you say the odds in favor of something happening, you are giving the ratio of a particular something happening to all possible happenings. For example, you can say the odds in favor of your football team winning is 1:20. When you say this, you mean that in your experience this football team will win one game and lose 20 other games, which are not very good odds in favor of. A better odds in favor of would be a doctor saying that your chances of getting better are 9:1, meaning that test results show nine people get better for every one person that doesn't.

Odds Against

On the flip side, when you say odds against, you are referring to the ratio of an event not happening to that event happening. For example, the odds against you winning the lottery would be 1 million:1. This means you have one million chances to lose and only one chance to win: this is not very likely to happen. Also, the doctor can say the odds against you getting better is 1:9 meaning you have one chance of not getting well and nine chances of getting better.

Odds against ratios are reversals of the odds in favor of ratios.

Part-to-Part and Part-to-Whole Ratios

Now that you know some common probability phrases, how can you understand these statements?

There are two ways you can visualize these statements. You can break them up into separate parts (part to part) or you can compare your probability part to a whole (part to whole). How likely something is to happen is determined by the size of your probability part.

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