This document discusses conditional probability and contingency tables. It defines conditional probability as the probability of an event given that another event has already occurred. Contingency tables collect data that shows different possible outcomes for different situations. Three examples are provided to demonstrate calculating conditional probabilities from contingency tables.

1. SECTION 12-3
CONDITIONAL PROBABILITY

2. ESSENTIAL QUESTIONS
• How do you find probabilities of events
given the occurrence of other events?
• How do you use contingency tables to find
conditional probabilities?

3. VOCABULARY
1. Conditional Probability:
2. Contingency Table:
3. Relative Frequency:

4. VOCABULARY
1. Conditional Probability:
2. Contingency Table:
3. Relative Frequency:
The probability of an
event given that another event has already
occurred

5. VOCABULARY
1. Conditional Probability:
2. Contingency Table:
3. Relative Frequency:
The probability of an
event given that another event has already
occurred P (B | A) =
P (A and B )
P (A)
,P (A) ≠ 0

6. VOCABULARY
1. Conditional Probability:
2. Contingency Table:
3. Relative Frequency:
The probability of an
event given that another event has already
occurred P (B | A) =
P (A and B )
P (A)
,P (A) ≠ 0
Collects the data that
shows how the different situations have
different possible outcomes

7. VOCABULARY
1. Conditional Probability:
2. Contingency Table:
3. Relative Frequency:
The probability of an
event given that another event has already
occurred P (B | A) =
P (A and B )
P (A)
,P (A) ≠ 0
Collects the data that
shows how the different situations have
different possible outcomes
How many times an
outcome occurs

8. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
a. He draws a heart given that the card is from a red
suit?

9. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
a. He draws a heart given that the card is from a red
suit?
P (heart | red)

10. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
a. He draws a heart given that the card is from a red
suit?
P (heart | red) =
P (red and heart)
P (red)

11. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
a. He draws a heart given that the card is from a red
suit?
P (heart | red) =
P (red and heart)
P (red)
=
13
26

12. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
a. He draws a heart given that the card is from a red
suit?
P (heart | red) =
P (red and heart)
P (red)
=
13
26
=
1
2

13. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
b. He draws an odd card given that the card is a
spade?

14. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
b. He draws an odd card given that the card is a
spade?
P (odd | spade)

15. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
b. He draws an odd card given that the card is a
spade?
P (odd | spade) =
P (spade and odd)
P (spade)

16. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
b. He draws an odd card given that the card is a
spade?
P (odd | spade) =
P (spade and odd)
P (spade)
=
4
13

17. EXAMPLE 1
Shecky draws a card from a standard deck of 52
cards. What is the probability of the following?
b. He draws an odd card given that the card is a
spade?
P (odd | spade) =
P (spade and odd)
P (spade)
=
4
13
≈ 30.8%

18. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138

19. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718

20. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289

21. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289
493

22. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289
493 514

23. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
P (college| girl)
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289
493 514

24. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
P (college| girl) =
P (college and girl)
P (girl)
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289
493 514

25. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
P (college| girl) =
P (college and girl)
P (girl)
=
376
514
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289
493 514

26. EXAMPLE 2
Find the probability that a student plans to attend
college after high school if the student is a girl.
P (college| girl) =
P (college and girl)
P (girl)
=
376
514
Going to
College
Number of Students
Boys Girls
Yes 342 376
No 151 138
718
289
493 514
≈ 73.2%

27. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256

28. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256
116

29. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256
116
1063

30. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256
116
1063
276

31. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256
116
1063
276 284

32. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256
116
1063
276 284 312

33. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
Class Freshman Sophomore Junior Senior
Varsity 7 22 36 51
Non-
varsity
269 262 276 256
116
1063
276 284 312 307

34. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.

35. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
P (non-varsity | senior)

36. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
P (non-varsity | senior)
=
P (non-varsity and senior)
P (senior)

37. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
P (non-varsity | senior)
=
P (non-varsity and senior)
P (senior)
=
256
307

38. EXAMPLE 3
Using the table below, find the probability that a
student is non-varsity given that he or she is a senior.
P (non-varsity | senior)
=
P (non-varsity and senior)
P (senior)
=
256
307
≈ 83.4%