Conditional probability worksheet for Statistics

Statistics treats conditional probability as the link between joint and single probabilities: P(A | B) = P(A and B) ÷ P(B). You use it with word problems and two-way tables, and run it backwards to find P(A and B).

Also taught in Algebra 2 and Geometry, each at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Conditional Probability Date Period Find each probability. Find a conditional probability from counts A survey of 16 families found that 12 pay for a video service and, of those, 7 also pay for a music service. Find the probability that a family pays for a music service given that they pay for a video service. In a group of 46 athletes, 12 play soccer but do not play basketball, 7 play basketball but do not play soccer, and 15 play both. Find the probability that an athlete plays basketball given that they play soccer. There are 21 students in a study. Of them, 11 belong to the robotics club and, of those, 7 also belong to the debate team. Find the probability that a student belongs to the debate team given that they belong to the robotics club. Of the 28 gardeners asked, 4 grow tomatoes but do not grow peppers, 10 grow peppers but do not grow tomatoes, and 4 grow both. Find the probability that a gardener grows tomatoes given that they grow peppers. In a group of 18 readers, 4 read science fiction and, of those, 2 also read mysteries. Find the probability that a reader reads mysteries given that they read science fiction. Of the 45 adults asked, 26 own a tablet, 29 own a laptop and 15 own both. Find the probability that an adult owns a laptop given that they own a tablet. A survey of 18 commuters found that 10 ride a bike and, of those, 2 also take the bus. Find the probability that a commuter takes the bus given that they ride a bike. Find a conditional probability from a two-way table $\begin{array}{ccc} Walk & Bus \\ Junior & 14 & 24 \\ Senior & 12 & 8 \end{array}$ Find $P ($ Junior $∣$ Bus $)$ . $\begin{array}{ccc} Walk & Bus \\ Junior & 22 & 36 \\ Senior & 26 & 29 \end{array}$ Find $P ($ Senior $∣$ Bus $)$ . $\begin{array}{ccc} Tea & Coffee \\ Morning & 23 & 7 \\ Evening & 32 & 12 \end{array}$ Find $P ($ Coffee $∣$ Morning $)$ . $\begin{array}{ccc} Beach & Mountains \\ Adult & 12 & 35 \\ Child & 14 & 40 \end{array}$ Find $P ($ Adult $∣$ Mountains $)$ . $\begin{array}{ccc} Beach & Mountains \\ Adult & 29 & 18 \\ Child & 15 & 38 \end{array}$ Find $P ($ Beach $∣$ Adult $)$ . $\begin{array}{ccc} Beach & Mountains \\ Adult & 13 & 19 \\ Child & 36 & 15 \end{array}$ Find $P ($ Mountains $∣$ Adult $)$ . $\begin{array}{ccc} Walk & Bus \\ Junior & 17 & 35 \\ Senior & 12 & 15 \end{array}$ Find $P ($ Walk $∣$ Junior $)$ . Use the conditional probability formula $P (A) = 0.9$ and $P (A$ and $B) = 0.27$ . Find $P (B ∣ A)$ . $P (A) = 0.2$ and $P (B ∣ A) = 0.4$ . Find $P (A$ and $B)$ . $P (A) = 0.6$ and $P (A$ and $B) = 0.36$ . Find $P (B ∣ A)$ . $P (A) = 0.5$ and $P (B ∣ A) = 0.7$ . Find $P (A$ and $B)$ . $P (A) = 0.9$ and $P (A$ and $B) = 0.18$ . Find $P (B ∣ A)$ . $P (A) = 0.5$ and $P (B ∣ A) = 0.1$ . Find $P (A$ and $B)$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Conditional Probability

Date Period

Find each probability.

Find a conditional probability from counts
A survey of 16 families found that 12 pay for a video service and, of those, 7 also pay for a music service. Find the probability that a family pays for a music service given that they pay for a video service.
In a group of 46 athletes, 12 play soccer but do not play basketball, 7 play basketball but do not play soccer, and 15 play both. Find the probability that an athlete plays basketball given that they play soccer.
There are 21 students in a study. Of them, 11 belong to the robotics club and, of those, 7 also belong to the debate team. Find the probability that a student belongs to the debate team given that they belong to the robotics club.
Of the 28 gardeners asked, 4 grow tomatoes but do not grow peppers, 10 grow peppers but do not grow tomatoes, and 4 grow both. Find the probability that a gardener grows tomatoes given that they grow peppers.
In a group of 18 readers, 4 read science fiction and, of those, 2 also read mysteries. Find the probability that a reader reads mysteries given that they read science fiction.
Of the 45 adults asked, 26 own a tablet, 29 own a laptop and 15 own both. Find the probability that an adult owns a laptop given that they own a tablet.
A survey of 18 commuters found that 10 ride a bike and, of those, 2 also take the bus. Find the probability that a commuter takes the bus given that they ride a bike.

Find a conditional probability from a two-way table
$\begin{array}{ccc} Walk & Bus \\ Junior & 14 & 24 \\ Senior & 12 & 8 \end{array}$ Find $P ($ Junior $∣$ Bus $)$ .
$\begin{array}{ccc} Walk & Bus \\ Junior & 22 & 36 \\ Senior & 26 & 29 \end{array}$ Find $P ($ Senior $∣$ Bus $)$ .
$\begin{array}{ccc} Tea & Coffee \\ Morning & 23 & 7 \\ Evening & 32 & 12 \end{array}$ Find $P ($ Coffee $∣$ Morning $)$ .
$\begin{array}{ccc} Beach & Mountains \\ Adult & 12 & 35 \\ Child & 14 & 40 \end{array}$ Find $P ($ Adult $∣$ Mountains $)$ .
$\begin{array}{ccc} Beach & Mountains \\ Adult & 29 & 18 \\ Child & 15 & 38 \end{array}$ Find $P ($ Beach $∣$ Adult $)$ .
$\begin{array}{ccc} Beach & Mountains \\ Adult & 13 & 19 \\ Child & 36 & 15 \end{array}$ Find $P ($ Mountains $∣$ Adult $)$ .
$\begin{array}{ccc} Walk & Bus \\ Junior & 17 & 35 \\ Senior & 12 & 15 \end{array}$ Find $P ($ Walk $∣$ Junior $)$ .

Use the conditional probability formula
$P (A) = 0.9$ and $P (A$ and $B) = 0.27$ . Find $P (B ∣ A)$ .
$P (A) = 0.2$ and $P (B ∣ A) = 0.4$ . Find $P (A$ and $B)$ .
$P (A) = 0.6$ and $P (A$ and $B) = 0.36$ . Find $P (B ∣ A)$ .
$P (A) = 0.5$ and $P (B ∣ A) = 0.7$ . Find $P (A$ and $B)$ .
$P (A) = 0.9$ and $P (A$ and $B) = 0.18$ . Find $P (B ∣ A)$ .
$P (A) = 0.5$ and $P (B ∣ A) = 0.1$ . Find $P (A$ and $B)$ .



Sigma Prep · sigmaprep.io/worksheets Name Conditional ProbabilityAnswer keyVersion 3 Date Period Find each probability. Find a conditional probability from counts A survey of 16 families found that 12 pay for a video service and, of those, 7 also pay for a music service. Find the probability that a family pays for a music service given that they pay for a video service. $\frac{7}{12}$ In a group of 46 athletes, 12 play soccer but do not play basketball, 7 play basketball but do not play soccer, and 15 play both. Find the probability that an athlete plays basketball given that they play soccer. $\frac{5}{9}$ There are 21 students in a study. Of them, 11 belong to the robotics club and, of those, 7 also belong to the debate team. Find the probability that a student belongs to the debate team given that they belong to the robotics club. $\frac{7}{11}$ Of the 28 gardeners asked, 4 grow tomatoes but do not grow peppers, 10 grow peppers but do not grow tomatoes, and 4 grow both. Find the probability that a gardener grows tomatoes given that they grow peppers. $\frac{2}{7}$ In a group of 18 readers, 4 read science fiction and, of those, 2 also read mysteries. Find the probability that a reader reads mysteries given that they read science fiction. $\frac{1}{2}$ Of the 45 adults asked, 26 own a tablet, 29 own a laptop and 15 own both. Find the probability that an adult owns a laptop given that they own a tablet. $\frac{15}{26}$ A survey of 18 commuters found that 10 ride a bike and, of those, 2 also take the bus. Find the probability that a commuter takes the bus given that they ride a bike. $\frac{1}{5}$ Find a conditional probability from a two-way table $\begin{array}{ccc} Walk & Bus \\ Junior & 14 & 24 \\ Senior & 12 & 8 \end{array}$ Find $P ($ Junior $∣$ Bus $)$ . $\frac{3}{4}$ $\begin{array}{ccc} Walk & Bus \\ Junior & 22 & 36 \\ Senior & 26 & 29 \end{array}$ Find $P ($ Senior $∣$ Bus $)$ . $\frac{29}{65}$ $\begin{array}{ccc} Tea & Coffee \\ Morning & 23 & 7 \\ Evening & 32 & 12 \end{array}$ Find $P ($ Coffee $∣$ Morning $)$ . $\frac{7}{30}$ $\begin{array}{ccc} Beach & Mountains \\ Adult & 12 & 35 \\ Child & 14 & 40 \end{array}$ Find $P ($ Adult $∣$ Mountains $)$ . $\frac{7}{15}$ $\begin{array}{ccc} Beach & Mountains \\ Adult & 29 & 18 \\ Child & 15 & 38 \end{array}$ Find $P ($ Beach $∣$ Adult $)$ . $\frac{29}{47}$ $\begin{array}{ccc} Beach & Mountains \\ Adult & 13 & 19 \\ Child & 36 & 15 \end{array}$ Find $P ($ Mountains $∣$ Adult $)$ . $\frac{19}{32}$ $\begin{array}{ccc} Walk & Bus \\ Junior & 17 & 35 \\ Senior & 12 & 15 \end{array}$ Find $P ($ Walk $∣$ Junior $)$ . $\frac{17}{52}$ Use the conditional probability formula $P (A) = 0.9$ and $P (A$ and $B) = 0.27$ . Find $P (B ∣ A)$ . $0.3$ $P (A) = 0.2$ and $P (B ∣ A) = 0.4$ . Find $P (A$ and $B)$ . $0.08$ $P (A) = 0.6$ and $P (A$ and $B) = 0.36$ . Find $P (B ∣ A)$ . $0.6$ $P (A) = 0.5$ and $P (B ∣ A) = 0.7$ . Find $P (A$ and $B)$ . $0.35$ $P (A) = 0.9$ and $P (A$ and $B) = 0.18$ . Find $P (B ∣ A)$ . $0.2$ $P (A) = 0.5$ and $P (B ∣ A) = 0.1$ . Find $P (A$ and $B)$ . $0.05$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Conditional ProbabilityAnswer keyVersion 3

Date Period

Find each probability.

Find a conditional probability from counts
A survey of 16 families found that 12 pay for a video service and, of those, 7 also pay for a music service. Find the probability that a family pays for a music service given that they pay for a video service. $\frac{7}{12}$
In a group of 46 athletes, 12 play soccer but do not play basketball, 7 play basketball but do not play soccer, and 15 play both. Find the probability that an athlete plays basketball given that they play soccer. $\frac{5}{9}$
There are 21 students in a study. Of them, 11 belong to the robotics club and, of those, 7 also belong to the debate team. Find the probability that a student belongs to the debate team given that they belong to the robotics club. $\frac{7}{11}$
Of the 28 gardeners asked, 4 grow tomatoes but do not grow peppers, 10 grow peppers but do not grow tomatoes, and 4 grow both. Find the probability that a gardener grows tomatoes given that they grow peppers. $\frac{2}{7}$
In a group of 18 readers, 4 read science fiction and, of those, 2 also read mysteries. Find the probability that a reader reads mysteries given that they read science fiction. $\frac{1}{2}$
Of the 45 adults asked, 26 own a tablet, 29 own a laptop and 15 own both. Find the probability that an adult owns a laptop given that they own a tablet. $\frac{15}{26}$
A survey of 18 commuters found that 10 ride a bike and, of those, 2 also take the bus. Find the probability that a commuter takes the bus given that they ride a bike. $\frac{1}{5}$

Find a conditional probability from a two-way table
$\begin{array}{ccc} Walk & Bus \\ Junior & 14 & 24 \\ Senior & 12 & 8 \end{array}$ Find $P ($ Junior $∣$ Bus $)$ . $\frac{3}{4}$
$\begin{array}{ccc} Walk & Bus \\ Junior & 22 & 36 \\ Senior & 26 & 29 \end{array}$ Find $P ($ Senior $∣$ Bus $)$ . $\frac{29}{65}$
$\begin{array}{ccc} Tea & Coffee \\ Morning & 23 & 7 \\ Evening & 32 & 12 \end{array}$ Find $P ($ Coffee $∣$ Morning $)$ . $\frac{7}{30}$
$\begin{array}{ccc} Beach & Mountains \\ Adult & 12 & 35 \\ Child & 14 & 40 \end{array}$ Find $P ($ Adult $∣$ Mountains $)$ . $\frac{7}{15}$
$\begin{array}{ccc} Beach & Mountains \\ Adult & 29 & 18 \\ Child & 15 & 38 \end{array}$ Find $P ($ Beach $∣$ Adult $)$ . $\frac{29}{47}$
$\begin{array}{ccc} Beach & Mountains \\ Adult & 13 & 19 \\ Child & 36 & 15 \end{array}$ Find $P ($ Mountains $∣$ Adult $)$ . $\frac{19}{32}$
$\begin{array}{ccc} Walk & Bus \\ Junior & 17 & 35 \\ Senior & 12 & 15 \end{array}$ Find $P ($ Walk $∣$ Junior $)$ . $\frac{17}{52}$

Use the conditional probability formula
$P (A) = 0.9$ and $P (A$ and $B) = 0.27$ . Find $P (B ∣ A)$ . $0.3$
$P (A) = 0.2$ and $P (B ∣ A) = 0.4$ . Find $P (A$ and $B)$ . $0.08$
$P (A) = 0.6$ and $P (A$ and $B) = 0.36$ . Find $P (B ∣ A)$ . $0.6$
$P (A) = 0.5$ and $P (B ∣ A) = 0.7$ . Find $P (A$ and $B)$ . $0.35$
$P (A) = 0.9$ and $P (A$ and $B) = 0.18$ . Find $P (B ∣ A)$ . $0.2$
$P (A) = 0.5$ and $P (B ∣ A) = 0.1$ . Find $P (A$ and $B)$ . $0.05$

How to do these

$P (A) = 0.5$ and $P (A$ and $B) = 0.2$ . Find $P (B ∣ A)$

Divide the overlap by the probability of the given event, A.
0.2 ÷ 0.5.

The answer is $0.4$ .

Where students go wrong

Dividing by the wrong event. In P(B | A) the given event is A, so divide by P(A); dividing by P(B) answers P(A | B) instead.

Also called probability of A given B, dependent probability or two-way table probability.

What you can put on this worksheet

Probability of A given B: In a group of 19 employees, 10 drive to work and, of those, 5 also work from home some days. Find the probability that an employee works from home some days given that they drive to work. → $\frac{1}{2}$
From a two-way table: $\begin{array}{ccc} Beach & Mountains \\ Adult & 25 & 31 \\ Child & 7 & 22 \end{array}$ Find $P ($ Adult $∣$ Mountains $)$ . → $\frac{31}{53}$
With the formula: $P (A) = 0.6$ and $P (A$ and $B) = 0.36$ . Find $P (B ∣ A)$ . → $0.6$
Conditional probability with P(A or B): $P (A) = 0.6$ , $P (B) = 0.6$ , and $P (A$ or $B) = 0.96$ . Find $P (A ∣ B)$ → $0.4$

Questions about these worksheets

Yes. Every conditional probability sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the conditional probability questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: probability of a given b, from a two-way table, with the formula and conditional probability with p(a or b). Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing by the whole group instead of the group the condition names. Given that they take Spanish, the denominator is the number of Spanish students, not the total.

Conditional probability worksheet for Statistics

Select your difficulty

Find a conditional probability from counts

Find a conditional probability from a two-way table

Use the conditional probability formula

Find a conditional probability from counts

Find a conditional probability from a two-way table

Use the conditional probability formula

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these conditional probability worksheets free?+

Do the conditional probability worksheets come with an answer key?+

Are these conditional probability worksheets printable?+

What grade are these conditional probability worksheets for?+

Can I get a different version of the same conditional probability worksheet?+

Is this a free alternative to Kuta Software for conditional probability?+

Can I choose how hard the conditional probability questions are?+

What kinds of question are on a conditional probability worksheet?+

What do students get wrong with conditional probability?+