Question

Suppose that E and F are two events and that N(E and F)=300 and N(E)=730. What is P(F|E)?

Answer 1

Answer:

$\displaystyle\frac{30}{73}$

Step-by-step explanation:

The formula of conditional probability is:

$\displaystyle P(F|E)=\frac{P(E \cap F)}{P(E)}$

And if we called N(U) the total number of possible outcomes, then remember by definition of probability:

$\displaystyle P(E \cap F)=\frac{N(E \cap F)}{N(U)}\\\displaystyle P(E)=\frac{N(E)}{N(U)}$

Then plugging them into the formula of conditional probability we get:

$\displaystyle P(F|E)=\frac{\frac{N(E \cap F)}{N(U)}}{\frac{N(E)}{N(U)}}$

Then we simplify and we get:

$\displaystyle P(F|E)=\frac{N(E \cap F)}{N(E)}$

We just plug the given info and we get:

$\displaystyle P(F|E)=\frac{300}{730}=\frac{30}{70}$