1. 12.3 Probability

2. Definition – Probability
When you toss a coin, there are only two possible outcomes – heads or tails. A desired outcome is called SUCCESS. Any other outcome is called FAILURE.
If an event can succeed in s ways and fail in f ways, then the probability of success, P(S), and of failure, P(F), are as follows:

3. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

4. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

5. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

6. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

7. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

8. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

9. Example 1
When two coins are tossed, what is the probability that both are tails?
Define success as HH and failure as all other options.

10. Example 2 – Probability with Combinations
Suppose you have 32 CDs – 18 Rock and 14 rap. Suppose that you randomly select 6 CDs to take on a trip. What is the probability that you select 3 Rock and 3 rap?

11. Example 2 – Probability with Combinations
Suppose you have 32 CDs – 18 Rock and 14 rap. Suppose that you randomly select 6 CDs to take on a trip. What is the probability that you select 3 Rock and 3 rap?
Step 1: Determine how many 6-CD selections meet this condition.

12. Example 2 – Probability with Combinations
Suppose you have 32 CDs – 18 Rock and 14 rap. Suppose that you randomly select 6 CDs to take on a trip. What is the probability that you select 3 Rock and 3 rap?
Step 1: Determine how many 6-CD selections meet this condition.

13. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.

14. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.

15. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.

16. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.
Step 3: Find the total number, s+f, of possible 6-CD selection.

17. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.
Step 3: Find the total number, s+f, of possible 6-CD selection.

18. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.
Step 3: Find the total number, s+f, of possible 6-CD selection.

19. Example 2
Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.
Step 3: Find the total number, s+f, of possible 6-CD selection.

20. Example 2
Step 4: Determine the probability.

21. Example 2
Step 4: Determine the probability.

22. Example 2
Step 4: Determine the probability.

23. Example 2
Step 4: Determine the probability.

24. Example 2 Step 4: Determine the probability.
The probability that you randomly select 3 Rock and 3 Rap CDs is

25. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

26. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

27. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

28. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

29. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

30. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

31. Calculator, How to [Math] button, then over to the PRB menu
Option 3 will compute the number of combinations for you “nCr”

32. Example 2
Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

33. Example 2
Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

34. Example 2
Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

35. Example 2
Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

36. Example 2
Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

37. Assignment