Question

which two statements about conditional probability are true?
a. conditional probability, (p(a)), is the probability that event a will occur.
b. conditional probability, (p(a|b)), is the probability that both event a and event b will occur.
c. conditional probability, (p(a|b)), is the probability of event a occurring given that event b has occurred.
d. the probability that it is raining outside is an example of conditional probability.
e. the probability that it is both raining and cloudy outside is an example of conditional probability.
f. the probability that it is raining if we already know it is cloudy outside is an example of conditional probability.

Explanation:

Conditional probability $P(A|B)$ is the probability of event $A$ occurring given that event $B$ has occurred. An example is the probability of it raining given that it is cloudy. Option A describes simple probability, not conditional. Option B is incorrect as $P(A|B)$ is not the probability of both $A$ and $B$ occurring. The probability of just it raining or it raining and being cloudy are not conditional probabilities in the described way.

Answer:

C. conditional probability, $P(A|B)$, is the probability of event $A$ occurring given that event $B$ has occurred.
F. The probability that it is raining if we already know it is cloudy outside is an example of conditional probability.