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Probability vs OddsTake a minute and think about the following questions:Have you ever encountered odds before? Where? When?Based on what you know, how are odds and probability similar?How are odds and probability different?Write your thoughts in your notebook or discuss them with a neighbor.What are our thoughts for each of these questions?Definition:OddsA ratio of the number of ways an event can occur versus the number of ways an event can’t occurOdds can be shown as a ratio or fractionEquations:Odds in Favor of an EventOdds in favor of event=number of ways it can occurnumber of ways it can't occurOdds Against an EventOdds against an event=number of ways it can't occurnumber of ways it can occurWhat’s the difference between these equations?Example:Imagine you are randomly choosing a letter from the alphabet. What are the odds in favor of choosing a vowel? What are the odds against choosing a vowel?To find the odds in favor of choosing a vowel, we need to know how many vowels and consonants there are in the alphabetOf the 26 letters, the vowels are A, E, I, O, U and Y so there are 6 vowels. That means there are 20 consonants.Odds in favor of a vowel=number of vowelsnumber of consonants=620 So the odds in favor of picking a vowel are 6:20 or 620To find the odds against choosing a vowel we simply use the other equationOdds against a vowel=number of consonantsnumber of vowels=206 So the odds against picking a vowel are 20:6 or 206Consider the following:What is the probability of choosing a vowel?How are the probability of choosing a vowel and the odds in favor of choosing a vowel related?How are the probability of choosing a vowel and the odds against choosing a vowel related?On your own or as a table, create a method for converting both types of odds into a probability.Let’s try a few together:During an experiment looking at drawing cards from a standard 52 card deck, the following data was collected:FrequencyRed107Queen20Red Jack6Face Card45King of Spades5Black Odd #47What is the percent probability of drawing a red card? What is the decimal probability of drawing a Queen? What is the ratio probability of drawing a red Jack? What are the odds in favor of drawing a face card? What are the odds in favor of drawing a King of Spades?What are the odds against drawing a black odd number? Try the question below on your own. If you can complete it correctly, you should be ready for the practice work.The probability of drawing a red 10 from a standard 52 card deck is 252. What are the odds against pulling a red 10?(25:1)PracticeComplete the Probability vs Odds Practice handout.Name:_______________ Date:_______________Probability vs Odds Practice HandoutThree R’s, three B’s and two Y’s are written on eight cards lying face down on a table. What is the:Probability of flipping an R?Odds in favor of flipping an R?Probability of flipping a Y?Odds against flipping a Y?There are 4 white, 14 blue and 5 green marbles in a bag. A marble is selected from the bag without looking. Find the odds of the following:Against picking a green marble.In favor of not picking a green marble.In favor of picking a white or blue marble.Describe the similarities or differences of the odds stated above.A die is rolled 50 times with the following data collected:FrequencyRolling less than 534Rolling a 47Rolling an even number24Determine the percent probability of rolling less than 5.Determine the odds against rolling a 4.Determine the odds in favor of rolling an even number. Express this as a ratio.According to Statistics Canada, there are 17,041,00 youth between the ages of 15 and 24 in Canada. Out of these youth, 1,274,300 are employed full-time, 1,177,000 are employed part-time and the rest are not employed. In your answers, express probabilities as percents and odds as ratios. Based on these statistics for 15 to 24 year olds:What is the probability of being employed full-time?What is the probability of being employed part-time?What is the probability of not being employed at all?What is the probability of being employed either full or part-time?What are the odds in favor of being employed?What are the odds against being employed? ................
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