Question

suppose that e and f are two events and that ( p(e) = 0.2 ) and ( p(f|e) = 0.5 ). what is ( p(e \text{ and } f) )?

( p(e \text{ and } f) = square )
(type an integer or a decimal. do not round)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(F|E)=\frac{P(E\cap F)}{P(E)}\).

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

Multiply both sides of the formula \(P(F|E)=\frac{P(E\cap F)}{P(E)}\) by \(P(E)\). We get \(P(E\cap F)=P(F|E)\times P(E)\).

Step3: Substitute the given values

Given \(P(E) = 0.2\) and \(P(F|E)=0.5\). Substitute these values into the formula \(P(E\cap F)=P(F|E)\times P(E)\). So \(P(E\cap F)=0.5\times0.2\).

Step4: Calculate the result

\(0.5\times0.2 = 0.1\).

Answer:

\(0.1\)