Question

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E|F) and P(F|E)

Answer 1

Hey mate

Good evening

There's the answer

Answer 2

$\bigstar$ Given:

Given that, $\sf{P(E)=0.6, \: P(F)= 0.3}$ and $\sf{P(E \cap F)=0.2}$

$\bigstar$ Solution:

We know that,

$P(A|B) = \frac{A \cap B}{P(B)}$

By substituting the values, we get

$\implies P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{0.2}{0.3} = \frac{2}{3}$

And, $\implies {P(F|E) = {\frac{P(E \cap E)}{P(F)} } = \sf\frac{0.2}{0.6} = \frac{1}{3}}$