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 · 3 with free solutions
Calculator allowed (Desmos)

Practise probability and conditional probability →Adaptive SAT module

What the test covers

Two-way tables, 'given that' questions

Key ideas

$P (A) = \frac{favourable}{total}$ .
'Given that' restricts the denominator to that row or column only.
Use the table totals; check they add up before calculating.

Common mistakes

$P (Grade 12 ∣ walks)$ 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.

IB link: IB SL 4.5-4.6.

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 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.

Student-produced response: type your answer.

Answer: 12/25 (also accepted: 0.48, .48, 48/100, 24/50)

$\frac{48}{100} = \frac{12}{25} = 0.48$ .

Practice questions

Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Solutions to the first 2 are open to everyone; the rest need only a free account. Every answer here was checked independently before it was published.

Question 1

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.

Student-produced response: type your answer.

Show the answer and solution

Answer: 2/3

There are $54$ Grade 11 students and $36$ of them walk: $\frac{36}{54} = \frac{2}{3}$ .

Question 2

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?

$\frac{9}{25}$
$\frac{3}{7}$
$\frac{4}{7}$
$\frac{9}{50}$

Show the answer and solution

Answer: B: $\frac{3}{7}$

Only the 84 students who play a team sport count; 36 of them are in Grade 12. $\frac{36}{84} = \frac{3}{7}$ .

Question 3

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.

Student-produced response: type your answer.

The solution is free with a free account.

Question 4

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.

Student-produced response: type your answer.

The solution is free with a free account.

Question 5

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.

Student-produced response: type your answer.

The solution is free with a free account.

Question 6

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.

Student-produced response: type your answer.

The solution is free with a free account.

Question 7

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?

$\frac{52}{171}$
$\frac{27}{79}$
$\frac{1}{2}$
$\frac{52}{79}$

The solution is free with a free account.

Question 8

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?

$\frac{29}{42}$
$\frac{58}{177}$
$\frac{13}{42}$
$\frac{58}{117}$

The solution is free with a free account.

Question 9

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?

$\frac{48}{83}$
$\frac{17}{33}$
$\frac{16}{33}$
$\frac{48}{191}$

The solution is free with a free account.

Question 10

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?

$\frac{25}{131}$
$\frac{4}{9}$
$\frac{5}{9}$
$\frac{25}{52}$

The solution is free with a free account.

Question 11

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?

$\frac{24}{43}$
$\frac{4}{11}$
$\frac{12}{17}$
$\frac{19}{43}$

The solution is free with a free account.

Keep going

The next College Board skill: notes, a Desmos tip and practice questions with solutions.

Next: Margin of error and inference

Previous: Two-variable data and models · Your SAT mistake log · Adaptive SAT Math module simulator · All SAT Math skills · Official SAT practice (Bluebook, Khan Academy) · SAT Reading and Writing · SAT prep home

SAT is a trademark registered by College Board, which is not affiliated with, and does not endorse, IB Math Revision. Every question here is our own.