Probability
# Conditional Probability

$H$ be the event you flip a heads and let $F$ be the event that you roll a 4. What is $P\left(H\ | \ F\right)?$

You flip a coin and roll a die. LetNote: $P\left(H\ | \ F\right)$ denotes the probability of $H$ occurring *given that* $F$ occurs.

A disease test is advertised as being 99% accurate: if you have the disease, you will test positive 99% of the time, and if you don't have the disease, you will test negative 99% of the time.

If 1% of all people have this disease and you test positive, what is the probability that you actually have the disease?

In general, the probability that it rains on Saturday is 25%.

If it rains on Saturday, the probability that it rains on Sunday is 50%. If it does not rain on Saturday, the probability that it rains on Sunday is 25%.

Given that it rained on Sunday, what is the probability that it rained on Saturday?