SAT Math: Probability and conditional probability
Probability and conditional probability, usually from a two-way table.
- Problem-Solving and Data Analysis · Probability and conditional probability
- Both modules
- 12 practice questions
- Calculator allowed (Desmos)
What the test covers
- Two-way tables, 'given that' questions
Key ideas
- \(P(A)=\dfrac{\text{favourable}}{\text{total}}\).
- 'Given that' restricts the denominator to that row or column only.
- Use the table totals; check they add up before calculating.
Common mistakes
- \(P(\text{Grade 12}\mid\text{walks})\) uses the 'walks' column total, not the grand total.
- Give probabilities as fractions or decimals, not percentages, in grid-ins.
Do it in Desmos
No Desmos needed: read the right row or column carefully.
Worked example
Worked example
The table shows the results of a survey of 200 students.
| Plays a team sport | Does not | Total | |
|---|---|---|---|
| Grade 11 | 48 | 52 | 100 |
| Grade 12 | 36 | 64 | 100 |
| Total | 84 | 116 | 200 |
A student who plays a team sport is chosen at random. What is the probability that the student is in Grade 12?
- \(\frac{9}{25}\)
- \(\frac{3}{7}\)
- \(\frac{4}{7}\)
- \(\frac{9}{50}\)
Answer: B: \(\frac{3}{7}\)
Only the 84 students who play a team sport count; 36 of them are in Grade 12. \(\tfrac{36}{84}=\tfrac37\).
Practice questions
Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Every answer here was re-checked independently by computer before it was published.
Question 1
The table shows the results of a survey of 200 students.
| Plays a team sport | Does not | Total | |
|---|---|---|---|
| Grade 11 | 48 | 52 | 100 |
| Grade 12 | 36 | 64 | 100 |
| Total | 84 | 116 | 200 |
A Grade 11 student is chosen at random. What is the probability that the student plays a team sport? Give your answer as a decimal or fraction.
Show the answer and solution
Answer: 12/25 (also accepted: 0.48, .48, 48/100, 24/50)
\(\tfrac{48}{100}=\tfrac{12}{25}=0.48\).
Question 2
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 27 | 40 | 67 |
| Grade 12 | 52 | 52 | 104 |
| Total | 79 | 92 | 171 |
A student who walks to school is chosen at random. What is the probability that the student is in Grade 12?
- \(\frac{52}{171}\)
- \(\frac{27}{79}\)
- \(\frac{1}{2}\)
- \(\frac{52}{79}\)
Show the answer and solution
Answer: D: \(\frac{52}{79}\)
Only the \(79\) students who walk count; \(52\) of them are in Grade 12: \(\tfrac{52}{79}=\frac{52}{79}\).
Question 3
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 26 | 34 | 60 |
| Grade 12 | 58 | 59 | 117 |
| Total | 84 | 93 | 177 |
A student who walks to school is chosen at random. What is the probability that the student is in Grade 12?
- \(\frac{29}{42}\)
- \(\frac{58}{177}\)
- \(\frac{13}{42}\)
- \(\frac{58}{117}\)
Show the answer and solution
Answer: A: \(\frac{29}{42}\)
Only the \(84\) students who walk count; \(58\) of them are in Grade 12: \(\tfrac{58}{84}=\frac{29}{42}\).
Question 4
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 51 | 57 | 108 |
| Grade 12 | 48 | 35 | 83 |
| Total | 99 | 92 | 191 |
A student who walks to school is chosen at random. What is the probability that the student is in Grade 12?
- \(\frac{48}{83}\)
- \(\frac{17}{33}\)
- \(\frac{16}{33}\)
- \(\frac{48}{191}\)
Show the answer and solution
Answer: C: \(\frac{16}{33}\)
Only the \(99\) students who walk count; \(48\) of them are in Grade 12: \(\tfrac{48}{99}=\frac{16}{33}\).
Question 5
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 20 | 59 | 79 |
| Grade 12 | 25 | 27 | 52 |
| Total | 45 | 86 | 131 |
A student who walks to school is chosen at random. What is the probability that the student is in Grade 12?
- \(\frac{25}{131}\)
- \(\frac{4}{9}\)
- \(\frac{5}{9}\)
- \(\frac{25}{52}\)
Show the answer and solution
Answer: C: \(\frac{5}{9}\)
Only the \(45\) students who walk count; \(25\) of them are in Grade 12: \(\tfrac{25}{45}=\frac{5}{9}\).
Question 6
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 38 | 26 | 64 |
| Grade 12 | 48 | 20 | 68 |
| Total | 86 | 46 | 132 |
A student who walks to school is chosen at random. What is the probability that the student is in Grade 12?
- \(\frac{24}{43}\)
- \(\frac{4}{11}\)
- \(\frac{12}{17}\)
- \(\frac{19}{43}\)
Show the answer and solution
Answer: A: \(\frac{24}{43}\)
Only the \(86\) students who walk count; \(48\) of them are in Grade 12: \(\tfrac{48}{86}=\frac{24}{43}\).
Question 7
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 12 | 14 | 26 |
| Grade 12 | 22 | 20 | 42 |
| Total | 34 | 34 | 68 |
A Grade 11 student is chosen at random. What is the probability that the student walks to school? Give your answer as a fraction or decimal.
Show the answer and solution
Answer: 6/13
There are \(26\) Grade 11 students and \(12\) of them walk: \(\tfrac{12}{26}=\frac{6}{13}\).
Question 8
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 24 | 14 | 38 |
| Grade 12 | 40 | 48 | 88 |
| Total | 64 | 62 | 126 |
A Grade 11 student is chosen at random. What is the probability that the student walks to school? Give your answer as a fraction or decimal.
Show the answer and solution
Answer: 12/19
There are \(38\) Grade 11 students and \(24\) of them walk: \(\tfrac{24}{38}=\frac{12}{19}\).
Question 9
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 18 | 14 | 32 |
| Grade 12 | 25 | 31 | 56 |
| Total | 43 | 45 | 88 |
A Grade 11 student is chosen at random. What is the probability that the student walks to school? Give your answer as a fraction or decimal.
Show the answer and solution
Answer: 9/16 (also accepted: .5625, 0.5625)
There are \(32\) Grade 11 students and \(18\) of them walk: \(\tfrac{18}{32}=\frac{9}{16}\).
Question 10
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 36 | 12 | 48 |
| Grade 12 | 28 | 29 | 57 |
| Total | 64 | 41 | 105 |
A Grade 11 student is chosen at random. What is the probability that the student walks to school? Give your answer as a fraction or decimal.
Show the answer and solution
Answer: 3/4 (also accepted: .75, 0.75)
There are \(48\) Grade 11 students and \(36\) of them walk: \(\tfrac{36}{48}=\frac{3}{4}\).
Question 11
The table shows the results of a survey of students.
| Walks to school | Does not | Total | |
|---|---|---|---|
| Grade 11 | 36 | 18 | 54 |
| Grade 12 | 40 | 41 | 81 |
| Total | 76 | 59 | 135 |
A Grade 11 student is chosen at random. What is the probability that the student walks to school? Give your answer as a fraction or decimal.
Show the answer and solution
Answer: 2/3
There are \(54\) Grade 11 students and \(36\) of them walk: \(\tfrac{36}{54}=\frac{2}{3}\).
Keep going
- Previous topic: Two-variable data and models
- Next topic: Margin of error and inference
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