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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 SATPractice 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

Dolphin question bank

Practice your skill

Question 1 of 3Easy
Among 24 students who play a sport, 15 also play an instrument. If a sport-playing student is selected, what is the probability the student plays an instrument?
  1. 3/8
  2. 5/8
  3. 15/40
  4. 24/15
Show answer and solution
Correct answerB. 5/8

Solution walkthrough

  1. The condition restricts the group to the 24 sport-playing students.
  2. Of those, 15 play an instrument, so 15/24 = 5/8.
Question 2 of 3Medium
A bag contains 4 red and 3 blue marbles. One red marble is removed. What is the probability the next marble is red?
  1. 1/3
  2. 1/2
  3. 3/7
  4. 4/7
Show answer and solution
Correct answerB. 1/2

Solution walkthrough

  1. After one red marble is removed, 3 red marbles remain among 6 total marbles, so the probability is 3/6 = 1/2.
Question 3 of 3Hard
In a survey of 100 commuters, 60 ride the bus and 30 both ride the bus and bike. Given that a commuter rides the bus, what is the probability the commuter also bikes?
  1. 3/10
  2. 1/2
  3. 3/5
  4. 9/10
Show answer and solution
Correct answerB. 1/2

Solution walkthrough

  1. The conditioned group is the 60 bus riders.
  2. Thirty of them also bike, so the probability is 30/60 = 1/2.

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

  1. Circle the condition introduced by given that, among, or if.
  2. Use only that group as the new sample space.
  3. Count the outcomes inside the group that also satisfy the requested event.
  4. 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.