SAT Math skill page

SAT Conditional Probability Practice

Restrict the sample space to the stated condition before counting favorable outcomes.

Practice conditional probability in Dolphin SAT Practice questions

12-18 min practice time3 questions on pageProblem Solving and Data Analysis

Practice time12-18 min

Question bank3 questions

Best forProblem Solving and Data Analysis

What this tests

What to know for this SAT skill

Recognize wording such as given that or among
Restrict the denominator to the conditioned group
Read joint counts from a two-way table
Update probabilities after an item is not replaced

Dolphin question bank

Practice your skill

Question 1 of 3Medium

A bag contains 3 red marbles and 2 blue marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are red?

$\frac{1}{5}$
$\frac{3}{10}$
$\frac{1}{2}$
$\frac{3}{5}$

Show answer and solution

Correct answerB. $\frac{3}{10}$

Solution walkthrough

The probability of drawing the first red marble is $\frac{3}{5}$ .
After drawing one red marble, there are 2 red marbles left out of 4 total marbles.
Thus, the probability of drawing a second red marble is $\frac{2}{4} = \frac{1}{2}$ .
Therefore, the probability that both marbles are red is $\frac{3}{5} \times \frac{1}{2} = \frac{3}{10}$ .

Question 2 of 3Medium

For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.

	\textbfRain	\textbfNo rain	\textbfTotal
\textbfNumber of weekdays	12	48	60
\textbfNumber of weekend days	8	16	24
\textbfTotal	20	64	84

If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?

$\frac{4}{21}$
$\frac{1}{4}$
$\frac{2}{3}$
$\frac{3}{4}$

Show answer and solution

Correct answer $B . \frac{1}{4}$

Solution walkthrough

There were 64 days with no rain.
It was a weekend day for 16 of those 64 days.
So 16 out of 64 of the days with no rain were weekend days.
Because the day is selected at random, each day has an equal chance of being selected, so the probability is $\frac{16}{64} = \frac{1}{4}$ .

Why the other choices miss

Choice A is incorrect. It is the probability that a day selected at random from any one of the days during the 12 weeks is a weekend day with no rain. Choice C is incorrect. It is the probability that a day selected at random from the weekend days has no rain. Choice D is incorrect. It is the probability that a day selected at random from the days with no rain is a weekday.

Question 3 of 3Medium

A bag contains 3 red balls and 2 blue balls. Two balls are drawn one after the other without replacement. What is the probability that both balls drawn are red?

$\frac{1}{5}$
$\frac{3}{10}$
$\frac{2}{5}$
$\frac{1}{2}$

Show answer and solution

Correct answerB. $\frac{3}{10}$

Solution walkthrough

To find the probability that both balls drawn are red, we use a tree diagram.
The probability of drawing a red ball first is $\frac{3}{5}$ .
After drawing one red ball, there are 2 red balls left out of a total of 4 balls.
Thus, the probability of drawing a second red ball is $\frac{2}{4} = \frac{1}{2}$ .
Therefore, the probability of both events occurring is $\frac{3}{5} \times \frac{1}{2} = \frac{3}{10}$ .

Avoid these traps

Common mistakes on this skill

Using the full sample as the denominator

The condition creates a smaller sample space, and that restricted group becomes the denominator.

Reversing the condition

The probability of biking given bus use is not automatically the same as bus use given biking.

Failing to update counts

Without replacement, both the category count and total count may change after the first selection.

Study plan

How to practice this skill in Dolphin

Circle the condition introduced by given that, among, or if.
Use only that group as the new sample space.
Count the outcomes inside the group that also satisfy the requested event.
Simplify the fraction and check that it matches the wording direction.

Practice conditional probability in Dolphin SAT

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FAQ

Questions about SAT Conditional Probability Practice

What does conditional probability mean?

It is the probability of an event after the sample space has been restricted by another known event or condition.

How do I recognize a conditional probability question?

Look for phrases such as given that, among those, if selected from, or after one item is removed.

How is this page different from basic probability practice?

Basic probability uses the full sample space. Conditional probability changes the sample space based on information in the question.