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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 SAT Try examples
12-18 min practice time 3 examples on page Problem Solving and Data Analysis
Practice time 12-18 min
On-page examples 3 examples
Best for Problem Solving and Data Analysis

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

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 explanation

Answer: 5/8

The condition restricts the group to the 24 sport-playing students. Of those, 15 play an instrument, so 15/24 = 5/8.

Example 2 Medium

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 explanation

Answer: 1/2

After one red marble is removed, 3 red marbles remain among 6 total marbles, so the probability is 3/6 = 1/2.

Example 3 Hard

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 explanation

Answer: 1/2

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

Quick drills

Practice this skill from more angles

Drill 1

Recognize wording such as given that or among

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 2

Restrict the denominator to the conditioned group

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 3

Read joint counts from a two-way table

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 4

Update probabilities after an item is not replaced

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

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.