10-7 Odds Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up A bag contains 15 nickels, 10 dimes, and 5 quarters. Two coins are drawn without replacement. 1. Find the probability that the first is a dime and the second is a quarter. 2. Find the probability that they are both nickels. Course Odds

Problem of the Day Larissa was born in August. What is the probability that she was born on an odd-numbered day? ≈ 0.52 Course Odds

Learn to convert between probabilities and odds. Course Odds

Vocabulary odds in favor odds against Insert Lesson Title Here Course Odds

Course Insert Lesson Title Here The odds in favor of an event is the ratio of favorable outcomes to unfavorable outcomes. The odds against an event is the ratio of unfavorable outcomes to favorable outcomes. odds in favor a:ba:ba:ba:b odds against b:ab:ab:ab:a a a = number of favorable outcomes b b = number of unfavorable outcomes a + b a + b = total number of outcomes

In a club raffle, 1,000 tickets were sold, and there were 25 winners. Estimate the odds in favor of winning this raffle. Additional Example 1A: Finding Odds Course Odds The number of favorable outcomes is 25, and the number of unfavorable outcomes is 1000 – 25 = 975. The odds in favor of winning this raffle are about 25 to 975, or 1 to 39.

In a club raffle, 1,000 tickets were sold, and there were 25 winners. Estimate the odds against winning this raffle. Additional Example 1B: Finding Odds Course Odds The odds in favor of winning this raffle are 1 to 39, so the odds against winning this raffle are about 39 to 1.

Of the 1750 customers at an arts and crafts show, 25 will win door prizes. Estimate the odds in favor winning a door prize. Check It Out: Example 1A Course Odds The number of favorable outcomes is 25, and the number of unfavorable outcomes is 1750 – 25 = The odds in favor of winning a door prize are about 25 to 1725, or 1 to 69.

Check It Out: Example 1B Course Odds Of the 1750 customers to an arts and crafts show, 25 will win door prizes. Estimate the odds against winning a door prize at the show. The odds in favor of winning a door prize are 1 to 69, so the odds against winning a door prize are about 69 to 1.

Course Odds Probability and odds are not the same thing, but they are related. Suppose you want to know the probability of rolling a 2 on a fair die. There is one way to get a 2 and five ways not to get a 2, so the odds in favor of rolling a 2 are 1:5. Notice the sum of the numbers in the ratio is the denominator of the probability. 1616

If the odds in favor of winning a CD player in a school raffle are 1:49, what is the probability of winning a CD player? Additional Example 2A: Converting Odds to Probabilities Course Odds On average there is 1 win for every 49 losses, so someone wins 1 out of every 50 times. P(CD player) = =

If the odds against winning the grand prize are 11,999:1, what is the probability of winning the grand prize? Additional Example 2B: Converting Odds to Probabilities Course Odds P(grand prize) = If the odds against winning the grand prize are 11,999:1, then the odds in favor of winning the grand prize are 1:11, ,999 1 = 12,000 1 ≈

Check It Out: Example 2A Course Odds If the odds in favor of winning a bicycle in a raffle are 1:75, what is the probability of winning a bicycle? On average there is 1 win for every 75 losses, so someone wins 1 out of 76 times. P(bicycle) = =

If the odds against winning the grand prize are 19,999:1, what is the probability of winning the grand prize? Check It Out: Example 2B Course Odds P(grand prize) = If the odds against winning the grand prize are 19,999:1, then the odds in favor of winning the grand prize are 1:19, ,999 1 = 20,000 1 ≈

Course Odds Suppose that the probability of an event is. This means that, on average, it will happen in 1 out of every 3 trials, and it will not happen in 2 out of every 3 trials, so the odds in favor of the event are 1:2 and the odds against the event are 2: CONVERTING PROBABILITIES TO ODDS If the probability of an event is, then the odds in favor of the event are m:(n – m) and the odds against the event are (n – m):m. mnmn

Additional Example 3: Converting Probabilities to Odds Course Odds On average, 1 out of every 20 people wins, and the other 19 people lose. The odds in favor of winning the meal are 1:(20 – 1), or 1:19. On average, 1 out of every 10 people wins, and the other 9 people lose. The odds against the door prize are (10 – 1):1, or 9:1. A. The probability of winning a free dinner is. What are the odds in favor of winning a free dinner? 1 20 B. The probability of winning a door prize is. What are the odds against winning a door prize? 1 10

Check It Out: Example 3 Course Odds A. The probability of winning a free laptop is. What are the odds in favor of winning a free laptop? 1 30 On average, 1 out of every 30 people wins, and the other 29 people lose. The odds in favor of winning the meal are 1:(30 – 1), or 1:29. On average, 1 out of every 50 people wins, and the other 49 people lose. The odds against the math book are (50 – 1 ):1, or 49:1. B. The probability of winning a math book is. What are the odds against winning a math book? 1 50

Lesson Quiz 19:1 1:19 Insert Lesson Title Here answer 4 Course Odds 599,999: Of 200 people at the grand opening of a store, 10 will win door prizes. 1. Estimate the odds of winning a door prize. 2. Estimate the odds against winning a door prize. 3. If the odds of winning a new computer are 1:899, what is the probability of winning the computer? 4. The probability of winning a new truck is. What are the odds against winning the truck? 1 600,000