1. 6.1 Introduction to Probability
Secondary Math 2
6.1 Introduction to Probability

2. Warm up What is half of one-third? What percent is 5 8 ?
What is 52% of 1,200?
What percent of 350 is 50?
What is one-third of two-fifths?

3. What is half of 0ne-third?

4. What is one-third of two-fifths?

5. What percent is 5 8 ?

6. What is 52% of 1200?

7. What percent of 350 is 50?

8. What you will learn
You will learn how to organize data, and how to compute the likelihood of some event happening.

9. Tuberculosis
Tuberculosis -- or TB, as it’s commonly called -- is a contagious infection that usually attacks the lungs. It can also spread to other parts of the body, like the brain and spine. A type of bacteria called Mycobacterium tuberculosis causes it.
In the 20th century, TB was a leading cause of death in the United States. Today, most cases are cured with antibiotics. But it takes a long time. You have to take meds for at least 6 to 9 months.

11. TB is contagious, but it’s not easy to catch. The germs grow slowly
TB is contagious, but it’s not easy to catch. The germs grow slowly. You usually have to spend a lot of time around a person who has it. That’s why it’s often spread among co- workers, friends, and family members. Tuberculosis germs don’t thrive on surfaces. You can’t get the disease from shaking hands with someone who has it, or by sharing their food or drink.

12. IF you thought you might have TB, wouldn’t you like to get tested?
Today’s task deals with the test results of tuberculosis.

13. There are different ways to organize data. This is called a tree.

14. Things to notice….if you add up ALL of the numbers, you get 2000, which is larger than our sample size, 1000.
What’s going on?

15. 2. A randomly selected person has TB.

16. 3. A randomly selected person Does Not Have TB.

17. 4. A randomly selected person Tests positive for TB but does NOT have it.

18. 5. A randomly selected person tested positive for TB, AND does have Tb.

19. 6. A Randomly selected person tested negative for TB, and does have tb.

20. 7. A Randomly selected person tested negative for TB, and does NOT have tb.

21. Probability Basics
What is probability? How likely something is to happen. Example: If I toss a coin, how likely is it that I will get a heads?

22. “What’s the chance of something happening?”
“There is a 100% chance it will rain today.”
There is less than a 5% chance you will be picked.
What is the smallest number that a probability can be?
What is the largest number that a probability can be?

23. How do we measure probability?
Probability Basics
How do we measure probability?
P(A)= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑖𝑡 𝑐𝑎𝑛 ℎ𝑎𝑝𝑝𝑒𝑛 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
fraction, decimal, %
*Chance of thunderstorms = 40%

24. Experiments and outcomes

25. Probability Basics
Example: there are 5 marbles in a bag. 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?
Total number of outcomes:
Total number of blue marbles:
Probability of drawing a blue marble:

26. Example: the chances of rolling a "4" with a 30-sided die.
Probability Basics
Example: the chances of rolling a "4" with a 30-sided die.
Total number of outcomes:
Total number of “4” happening:
Probability of rolling a 4:

27. Probability is always between 0 and 1
Probability Basics
We can show probability on a Probability Line:
Probability is always between 0 and 1

28. Probability Basics
Note: Probability is just a guide! Probability does not tell us exactly what will happen, it is just a guide (think the ‘odds’ long-term)

29. Probability Basics
Ways to organize data…you should have seen a few last year. Do you remember any? This year, we will be working with three of these organizational tools.

30. Diagrams
Diagrams are often the key to getting started on a problem. (they are like our pictures for our word problems) They can clarify relationships that appear complicated when written.

31. Probability Basics
Tree Diagrams

32. Probability Basics
Venn Diagrams

33. Two-way frequency tables
Probability Basics
Two-way frequency tables
Do you know how to find the missing data?
Male
Female
Total
Walk 46
Car 28
 17 45
Bus 12 27
Bike 69
129 92

34. Your Turn - #1
Draw a tree diagram representing the outcomes for flipping a coin, then tossing a die.
a) How many outcomes are there?
b) What is the probability of getting heads, then an even number.

35. Try out NUMBER 2

36. ‘and’ verses ‘or’
AND = Intersection = (∩) = (multiply the different probabilities)
2c) what is the probability that a student passes both tests?
OR = Union (∪) = (add the different probabilities)
2d) what is the probability that a student passes only one of the tests?