The rules that solve most questions
- Probability = (number of favorable outcomes) / (number of outcomes in the group you're choosing from).
- Conditional probability: restrict the denominator to the given group, the row or column total.
- "And" means one cell of the table; "or" means add the cells without double-counting.
Traps the wrong answers are built on
- Using the grand total when the question restricts the group.
- Using the row total when the question restricts to a column.
Worked example
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
| Art | Music | Total | |
|---|---|---|---|
| 9th grade | 30 | 32 | 62 |
| 10th grade | 20 | 34 | 54 |
| Total | 50 | 66 | 116 |
If a 10th grader in the survey is chosen at random, what is the probability that the student prefers music?
- A. 17/58
- B. 10/27
- C. 17/27
- D. 17/33
Answer: C. "Given" narrows the group: only the 54 students in that row count. Of those, 34 match. Probability = 34/54 = 17/27.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Medium
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 30 32 62 10th grade 20 34 54 Total 50 66 116 If a 10th grader in the survey is chosen at random, what is the probability that the student prefers music?
Show answer and explanation
Answer: C
"Given" narrows the group: only the 54 students in that row count.
Of those, 34 match.
Probability = 34/54 = 17/27.
- Question 2Medium
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 36 38 74 10th grade 19 30 49 Total 55 68 123 If a 10th grader in the survey is chosen at random, what is the probability that the student prefers music?
Show answer and explanation
Answer: D
"Given" narrows the group: only the 49 students in that row count.
Of those, 30 match.
Probability = 30/49.
- Question 3Easier
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 39 13 52 10th grade 26 26 52 Total 65 39 104 If a student in the survey is chosen at random, what is the probability that the student is a 9th grader who prefers music?
Show answer and explanation
Answer: B
The whole survey is the group: 104 students.
Of those, 13 match.
Probability = 13/104 = 1/8.
- Question 4Easier
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 10 31 41 10th grade 39 40 79 Total 49 71 120 If a student in the survey is chosen at random, what is the probability that the student is a 9th grader who prefers music?
Show answer and explanation
Answer: B
The whole survey is the group: 120 students.
Of those, 31 match.
Probability = 31/120.
- Question 5Medium
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 18 37 55 10th grade 17 14 31 Total 35 51 86 If a student who prefers art is chosen at random, what is the probability that the student is in 9th grade?
Show answer and explanation
Answer: D
"Given" narrows the group: only the 35 students in that column count.
Of those, 18 match.
Probability = 18/35.
- Question 6Medium
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 25 19 44 10th grade 16 34 50 Total 41 53 94 If a 10th grader in the survey is chosen at random, what is the probability that the student prefers music?
Show answer and explanation
Answer: C
"Given" narrows the group: only the 50 students in that row count.
Of those, 34 match.
Probability = 34/50 = 17/25.
- Question 7Easier
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 29 19 48 10th grade 36 19 55 Total 65 38 103 If a student in the survey is chosen at random, what is the probability that the student is a 9th grader who prefers music?
Show answer and explanation
Answer: D
The whole survey is the group: 103 students.
Of those, 19 match.
Probability = 19/103.
- Question 8Easier
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 28 19 47 10th grade 15 17 32 Total 43 36 79 If a student in the survey is chosen at random, what is the probability that the student is a 9th grader who prefers music?
Show answer and explanation
Answer: C
The whole survey is the group: 79 students.
Of those, 19 match.
Probability = 19/79.
- Question 9Easier
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 32 37 69 10th grade 34 13 47 Total 66 50 116 If a student in the survey is chosen at random, what is the probability that the student is a 9th grader who prefers music?
Show answer and explanation
Answer: D
The whole survey is the group: 116 students.
Of those, 37 match.
Probability = 37/116.
- Question 10Medium
A survey asked students in two grades whether they prefer art or music. The results are shown in the table.
Art Music Total 9th grade 24 26 50 10th grade 28 39 67 Total 52 65 117 If a student who prefers art is chosen at random, what is the probability that the student is in 9th grade?
Show answer and explanation
Answer: D
"Given" narrows the group: only the 52 students in that column count.
Of those, 24 match.
Probability = 24/52 = 6/13.
More Problem-Solving and Data Analysis practice
Questions people ask
Is this probability and conditional probability practice like the real SAT?
The questions follow the format of the digital SAT's Problem-Solving and Data Analysis domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Problem-Solving and Data Analysis is one of the four content domains of the SAT Math section, alongside Algebra, Advanced Math, Geometry and Trigonometry.