GOZUNTA
Try it now
All courses Math II · S-CP.6 68 of 73
Compute conditional probability as the fraction of one event's outcomes that also belong to another event.

Compute conditional probability from a finite sample space by restricting to the given event

Problem
In S=1,2,3,4,5,6, restrict to outcomes greater than 3, then count the even outcomes within that conditioned set to find P(even|greater than 3).
Your answer
Show answer choicesAnswer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Choose exactly what to practice.

Browse the learning objectives and included problem types, then build a session around the math you want to work on.

Create a free account
With paid access

Use the complete visual-support library.

Paid access opens the visual supports attached throughout the full problem bank in your subscribed course or courses.

Compare plans

Hint

Start with the condition “greater than 3,” then keep only those outcomes.

For \(P(A|B)\), restrict the sample space to \(B\) first, then count how many of those outcomes are also in \(A\).

Solution walkthrough

01

Restrict to the condition

\[\text{greater}~\text{than}~3~->~{4,5,6}\]

Conditional probability discards outcomes that do not satisfy the condition before counting the target event.

02

Count the conditioned sample space

\[\text{there}~\text{are}~3~\text{outcomes}\]

The new denominator is 3, not the original sample-space size 6.

03

Find even outcomes within it

\[{4,6},~\text{so}~\text{favorable}~\text{count}=2\]

Four and six are even; five is not.

04

Form and interpret

\[P(\text{even}|\text{greater}~\text{than}~3)=2/3\]

Two of the three outcomes in the restricted set are even.

+

Another way

  1. Use intersection 4,6 over condition set 4,5,6.

!

Common mistake

Do not use all six outcomes in the denominator after conditioning.