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### Probability vs. Odds

Calculating One Given the Others

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

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.

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.

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.

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

- If the probability of an event is 2/3, what are the odds of this event?

20

Additional ExampleThe 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.

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.

Video Explanation

- Click here for a video explaining how to solve these types of problems
(Ignore the part that talks about Odds against)

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.

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

- If the odds of an event is 2:3, what is the probability of this event?

1

50

1

1 + 49

Additional ExampleIf 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) =

1

76

1

1 + 75

Another ExampleIf 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.

Video Explanation

- Click here for a video explaining how to solve these types of problems

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.

Homework

- Complete the Probability vs. Odds assignment now.

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