SAT
Find the probability of one event, given that the other event occurred.
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Given that
The words given that tell you which group to use.
The total is the total of that row or that column.
Favorable is the cell in that group for the other event.
Probability = favorablegiven total
One worked example
The table shows the number of students in band.
| Grade | In band | Not in band | Total |
|---|---|---|---|
| 9th grade | 12 | 18 | 30 |
| 10th grade | 16 | 14 | 30 |
| Total | 28 | 32 | 60 |
One student is selected at random. What is the probability that the student is in band, given that the student is in 9th grade?
Given that the student is in 9th grade, use only the 9th grade row.
The 9th grade total is 30 students.
Of those, 12 are in band.
Probability = favorablegiven total
= 1230
= 25
Work these three in a session.
The table shows the number of students at each practice.
| Practice | Soccer | Tennis | Total |
|---|---|---|---|
| Monday | 14 | 10 | 24 |
| Friday | 6 | 10 | 16 |
| Total | 20 | 20 | 40 |
One student is selected at random. What is the probability that the student plays soccer, given that the student practices on Monday?
Given that the student practices on Monday, use only the Monday row.
The Monday total is 24 students.
Of those, 14 play soccer.
Probability = favorablegiven total
= 1424
= 712
The grand total counts the whole table. This question uses only the Monday row.
Answer: B. 712
The table shows where students sit on the bus.
| Seat | Window | Aisle | Total |
|---|---|---|---|
| Front | 8 | 12 | 20 |
| Back | 16 | 12 | 28 |
| Total | 24 | 24 | 48 |
One student is selected at random. What is the probability that the student sits in the back, given that the student has a window seat?
Given that the student has a window seat, use only the Window column.
The Window total is 24 students.
Of those, 16 sit in the back.
Probability = favorablegiven total
= 1624
= 23
The grand total counts the whole table. This question uses only the Window column.
Answer: D. 23
The table shows the books in a classroom library.
| Book | Fiction | Facts | Total |
|---|---|---|---|
| Paperback | 18 | 12 | 30 |
| Hardcover | 10 | 20 | 30 |
| Total | 28 | 32 | 60 |
One book is selected at random. What is the probability that the book is fiction, given that the book is a paperback?
Given that the book is a paperback, use only the Paperback row.
The Paperback total is 30 books.
Of those, 18 are fiction.
Probability = favorablegiven total
= 1830
= 35
The grand total counts the whole table. This question uses only the Paperback row.
Answer: A. 35
Try these five on your own.
The table shows the writing hand of students in two classes.
| Class | Left | Right | Total |
|---|---|---|---|
| Ceramics | 9 | 15 | 24 |
| Theater | 6 | 18 | 24 |
| Total | 15 | 33 | 48 |
One student is selected at random. What is the probability that the student writes with the left hand, given that the student is in ceramics?
Given that the student is in ceramics, use only the Ceramics row.
The Ceramics total is 24 students.
Of those, 9 write with the left hand.
Probability = favorablegiven total
= 924
= 38
The grand total counts the whole table. This question uses only the Ceramics row.
Answer: C. 38
The table shows the shirts for sale.
| Size | Red | Blue | Total |
|---|---|---|---|
| Small | 8 | 10 | 18 |
| Large | 10 | 12 | 22 |
| Total | 18 | 22 | 40 |
One shirt is selected at random. What is the probability that the shirt is large, given that the shirt is red?
Given that the shirt is red, use only the Red column.
The Red total is 18 shirts.
Of those, 10 are large.
Probability = favorablegiven total
= 1018
= 59
The grand total counts the whole table. This question uses only the Red column.
Answer: D. 59
The table shows the students who signed up for a weekend activity.
| Day | Indoor | Outdoor | Total |
|---|---|---|---|
| Saturday | 10 | 18 | 28 |
| Sunday | 14 | 8 | 22 |
| Total | 24 | 26 | 50 |
One student is selected at random. What is the probability that the student chose an indoor activity, given that the student signed up for Saturday?
Given that the student signed up for Saturday, use only the Saturday row.
The Saturday total is 28 students.
Of those, 10 chose an indoor activity.
Probability = favorablegiven total
= 1028
= 514
The grand total counts the whole table. This question uses only the Saturday row.
Answer: B. 514
The table shows the lunches students chose.
| Grade | Hot lunch | Packed lunch | Total |
|---|---|---|---|
| 4th grade | 24 | 6 | 30 |
| 5th grade | 16 | 14 | 30 |
| Total | 40 | 20 | 60 |
One student is selected at random. What is the probability that the student is in 5th grade, given that the student chose a packed lunch?
Given that the student chose a packed lunch, use only the Packed lunch column.
The Packed lunch total is 20 students.
Of those, 14 are in 5th grade.
Probability = favorablegiven total
= 1420
= 710
The grand total counts the whole table. This question uses only the Packed lunch column.
Answer: A. 710
The table shows the pets students have at home.
| Home | Cat | Dog | Total |
|---|---|---|---|
| Apartment | 9 | 15 | 24 |
| House | 21 | 15 | 36 |
| Total | 30 | 30 | 60 |
One student is selected at random. What is the probability that the student lives in an apartment, given that the student has a cat?
Given that the student has a cat, use only the Cat column.
The Cat total is 30 students.
Of those, 9 live in an apartment.
Probability = favorablegiven total
= 930
= 310
The grand total counts the whole table. This question uses only the Cat column.
Answer: C. 310
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