Question

Suppose that E and f are two events and that P(E and F)=0.3 and P(E)=0.5. What is P(F/E)?

Answer 1

Answer:

$P(F/E) = 0.6$

Step-by-step explanation:

If we are given two dependent events $A$ and $B$ such that their chances of occurrence or the probabilities of the events are: $P(A)$ and $P(B)$.

Then the conditional probability that the event $B$ will occur given that $A$ has already occurred is given by the following formula:

$P(B/A) = \dfrac{P(A \cap B)}{P(A)}$

Here the two events given are $E$ and $F$.

$P(E\ and\ F)\ or\ P(E\cup F) = 0.3$

and $P(E) = 0.5$

As per the above formula that we have already discussed, the formula can be written as:

$P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}$