Question

suppose that e and f are two events and that p(e)=0.1 and p(f|e)=0.4. what is p(e and f)?
p(e and f)=
(simplify your answer.)

Explanation:

Step1: Recall conditional - probability formula

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

Step2: Solve for $P(E\cap F)$

We can re - arrange the formula to get $P(E\cap F)=P(F|E)\times P(E)$.

Step3: Substitute given values

Given $P(E) = 0.1$ and $P(F|E)=0.4$, we substitute these values into the formula: $P(E\cap F)=0.4\times0.1$.

Step4: Calculate the result

$P(E\cap F)=0.04$.

Answer:

$0.04$