GOZUNTA
Try it now
All courses Geometry · S-CP.7 46 of 57
Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).

Use the Addition Rule to find P(A or B) for overlapping events

Problem
Use \(P(A~\text{or}~B)=P(A)+P(B)-P(A~\text{and}~B)\) with \(0.50\), \(0.30\), and overlap \(0.10\). Compute the union without double-counting the overlap.
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Practice the problem type you meant to practice.

Navigate by objective and problem type instead of taking whichever free problem happens to come next.

Create a free account
With paid access

Give your progress record more evidence.

A larger problem bank gives you more chances to see whether a skill is becoming dependable.

Compare plans

Hint

Use the addition rule for overlapping events: \(P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)\).

Subtract the overlap once because adding \(P(A)\) and \(P(B)\) counts the intersection twice.

Solution walkthrough

01

Use the overlapping-events addition rule

\[P(A~\text{or}~B)=P(A)+P(B)-P(A~\text{and}~B)\]

Adding both event probabilities counts overlap twice, so subtract it once.

02

Substitute

\[0.50+0.30-0.10\]

The source values are P(A)=0.50, P(B)=0.30, and joint probability 0.10.

03

Calculate

\[0.80-0.10=0.70\]

The inclusive union probability is 0.70.

04

Check bounds

\[0.50\le~0.70\le~0.80\]

The union is at least each marginal and no more than their uncorrected sum, a necessary consistency check.

+

Another way

  1. Break the union into A-only 0.40, overlap 0.10, and B-only 0.20, then add.

!

Common mistake

Do not stop at 0.80; that double-counts the overlap.

Solution walkthrough video