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 event $B$ has occurred. An example is the probability of rain given it is cloudy. Option A is just the probability of $A$ (not conditional). Option B is the joint - probability $P(A\cap B)$. The probability of rain alone or rain and cloud together are not conditional probabilities in the described sense.

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.