Question

if ( p(e) = 0.45 ), ( p(e \text{ or } f) = 0.50 ), and ( p(e \text{ and } f) = 0.15 ), find ( p(f) )

( p(f)=square ) (simplify your answer)

Explanation:

Step1: Use the formula for \(P(E\ or\ F)\)

The formula is \(P(E\ or\ F)=P(E)+P(F)-P(E\ and\ F)\).

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

We get \(P(F)=P(E\ or\ F)+P(E\ and\ F)-P(E)\).

Step3: Substitute the given values

Substitute \(P(E) = 0.45\), \(P(E\ or\ F)=0.50\), and \(P(E\ and\ F)=0.15\) into the formula:
\(P(F)=0.50 + 0.15-0.45\).

Step4: Calculate the value

\(P(F)=0.2\).

Answer:

\(0.2\)