Question

use the addition rule to solve the given problem.
if ( p(e)=0.2, p(f)=0.6 ), and ( p(e cup f)=0.4 ), then what is ( p(e cap f) )?
( p(e cap f)=quad ) (type an integer or a decimal )
help me solve this view an example get more help

Explanation:

Step1: Recall the addition rule formula

The addition rule for probability is \(P(E\cup F)=P(E)+P(F)-P(E\cap F)\).

Step2: Rearrange the formula to solve for \(P(E\cap F)\)

We can rewrite the formula as \(P(E\cap F)=P(E)+P(F)-P(E\cup F)\).

Step3: Substitute the given values

Substitute \(P(E) = 0.2\), \(P(F)=0.6\), and \(P(E\cup F)=0.4\) into the formula:
\(P(E\cap F)=0.2 + 0.6-0.4\).

Step4: Calculate the result

\(0.2+0.6 = 0.8\), then \(0.8 - 0.4=\boldsymbol{0.4}\).

Answer:

\(0.4\)