Probability vs. Odds

1. Calculating One Given the Others Probability vs. Odds

2. Probability Review Divided By Probability = Success / Total • Example: If you have 6 socks and 2 are red, what is the probability of randomly choosing a red sock? • Success=Red Sock=2 • Total=Total Socks=6 • Probability of choosing a red sock? • 2/6 → 1/3

3. Your Turn to Try Wow! • If you have 18 marbles and 3 of them are red, 6 are blue and 9 are yellow, what is the probability of randomly choosing a red one? A. 1/6 B. 1/3 Remember success is the number of red marbles and total is the total number of Marbles. You may need to reduce your answer. Try again. C. 1/18 D. 1/2 Click on the option above that you think is the correct answer.

4. Odds Review Odds = Success : Failure • Example: If you have 6 socks and 2 are red, what are the odds of randomly choosing a red sock? • Success=red sock=2 • Failure=non-red socks=4 • Probability of choosing red sock? • 2:4 → 1:2 Number of ways the event can occur : compared to the number of ways the event can fail.

5. Your Turn to Try Super • If you have 18 marbles and 3 of them are red, 6 are blue and 9 are yellow, what are the odds of randomly choosing a red one? A. 1:6 Remember success is the number of red marbles and failure is the number of non-red marbles. You may need to reduce your answer. Try again. B. 1:18 C. 1:2 D. 1:5 Click on the option above that you think is the correct answer.

6. Calculating Odds Given Probability • Example: • If the probability of an event is 2/3, what are the odds of this event? • Remember that probability is success/total. • If the total = 3 and the success = 2, failure is total-success = 3-2 =1 • Odds = success : failure = 2:1

7. 1 20 Additional Example The probability of winning a free dinner is . What are the odds of winning a free dinner? On average, 1 out of every 20 people wins, and the other 19 people lose. The odds in favor of winning the meal are1:(20 – 1), or 1:19.

8. 1 30 Another Example The probability of winning a free laptop is . What are the odds of winning a free laptop? On average, 1 out of every 30 people wins, and the other 29 people lose. The odds in favor of winning the laptop are 1:(30 – 1), or 1:29.

9. Video Explanation • Click here for a video explaining how to solve these types of problems (Ignore the part that talks about Odds against)

10. Your Turn to Try Great! • If the probability of an event are 2/5, what are the odds of this event? A. 3:2 Remember to find the failure, you need to subtract total-success B. 2:7 C. 2:3 D. 5:3 Click on the option above that you think is the correct answer.

11. Calculating Probability Given Odds • Example: • If the odds of an event is 2:3, what is the probability of this event? • Remember that odds is success : failure • If the failure = 3 and the success = 2, total is failure + success = 3+2 = 5 • Probability = success / total = 2/5

12. = 1 50 1 1 + 49 Additional Example If the odds of winning a CD player in a school raffle are 1:49, what is the probability of winning a CD player? On average there is 1 win for every 49 losses, so someone wins 1 out of every 50 times. P(CD player) =

13. = 1 76 1 1 + 75 Another Example If the odds of winning a bicycle in a raffle are 1:75, what is the probability of winning a bicycle? P(bicycle) = Hint: On average there is 1 win for every 75 losses, so someone wins 1 out of 76 times.

14. Video Explanation • Click here for a video explaining how to solve these types of problems

15. Your Turn to Try Cool! • If the Odds of an event are 2:5, what is the probability of this event? A. 3/2 Remember to find the total, you need to add failure + success B. 2/7 C. 2/3 D. 5/3 Click on the option above that you think is the correct answer.

16. Homework • Complete the Probability vs. Odds assignment now.