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However, the total number of favorable outcomes isn't 13 + 4 + 4 = 21. There are thirteen diamonds in the deck, four kings, and four eights. For instance, if you're playing poker and you have a nine, ten, jack, and queen of diamonds in your hand, you want your next card either to be a king or eight of any suit (to make a straight), or, alternatively, any diamond (to make a flush.) Let's say the dealer is dealing your next card from a standard fifty-two card deck. X Research source Sometimes, certain outcomes can overlap - the odds you calculate should reflect this. Your odds of rolling a "yahtzee" (five dice that are all the same number) in one roll are very slim - 6 : 6 5 - 6 = 6 : 7770 = 1 : 1295!

Odds change exponentially based on the number of events occurring simultaneously.

So the odds of rolling a combined "four" with two dice are 3 : (36-3) = 3 : 33 = 1 : 11 Next, find the number of ways you can make four with two dice: you can roll a 1 and a 3, a 2 and a 2, or a 3 and a 1 - three ways. Take the number of outcomes for each die to the power of the number of dice: 6(number of sides on each die) 2(number of dice) = 36 possible outcomes. To calculate the odds of rolling two dice with a sum of four (for instance, a 1 and a 3), begin by calculating the total number of outcomes. In this case, the odds for each sum should reflect the fact that some outcomes are more likely than others. For instance, you could roll a 1 and a 6, a 2 and a 5, a 3 and a 4, and so on. By contrast, there are many ways to make a seven. There's only one way to make 2 - by rolling two 1's - and there's only one way to make 12 - by rolling two 6's. However, if we roll two dice and add their numbers together, though there's a chance we'll get anything from 2 to 12, not every outcome is equally likely. X Research source If we roll one die, it's equally likely that we'll get any of the numbers 1 - 6. A formula for calculating probability from odds is P = O / (O + 1).ĭetermine whether all outcomes are equally likely.

A simple formula for calculating odds from probability is O = P / (1 - P).

Probability can be expressed as 9/30 = 3/10 = 30% - the number of favorable outcomes over the number of total possible outcomes. The answer is the total number of outcomes.

Add the numerator (9) and denominator (21) : 9 + 21 = 30. To find probability from a given odds ratio, first express your odds as a fraction (we'll use 9 / 21 ).Odds can then be expressed as 5 : 8 - the ratio of favorable to unfavorable outcomes. The answer is the number of unfavorable outcomes. Subtract the numerator (5) from the denominator (13) : 13 - 5 = 8. To find an odds ratio from a given probability, first express the probability as a fraction (we'll use 5/13). It's easy to convert between probability and odds.X Expert Source David JiaĪcademic Tutor Expert Interview. So our 1 : 2 odds of winning translate to a 33% chance that we'll win. In our example, the probability (not odds) that we'll roll a one or a two (out of six possible die roll outcomes) is 2 / 6 = 1 / 3 =. This is found by dividing the number of desired outcomes over the total number of possible outcomes.

Probability is simply a representation of the chance that a given outcome will happen. X Research source The concepts of odds and probability are related, but not identical. Know the difference between odds and probability. This article has been viewed 801,650 times. In this case, several readers have written to tell us that this article was helpful to them, earning it our reader-approved status. WikiHow marks an article as reader-approved once it receives enough positive feedback. There are 14 references cited in this article, which can be found at the bottom of the page. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more.

David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. This article was co-authored by David Jia.