which two statements about conditional probability are true?\na. conditional probability, (p(a)), is the…

which two statements about conditional probability are true?\na. conditional probability, (p(a)), is the probability that event (a) will occur.\nb. conditional probability, (p(a|b)), is the probability that both event (a) and event (b) will occur.\nc. conditional probability, (p(a|b)), is the probability of event (a) occurring given that event (b) has occurred.\nd. the probability that it is raining outside is an example of conditional probability.\ne. the probability that it is both raining and cloudy outside is an example of conditional probability.\nf. the probability that it is raining if we already know it is cloudy outside is an example of conditional probability.

which two statements about conditional probability are true?\na. conditional probability, (p(a)), is the probability that event (a) will occur.\nb. conditional probability, (p(a|b)), is the probability that both event (a) and event (b) will occur.\nc. conditional probability, (p(a|b)), is the probability of event (a) occurring given that event (b) has occurred.\nd. the probability that it is raining outside is an example of conditional probability.\ne. the probability that it is both raining and cloudy outside is an example of conditional probability.\nf. the probability that it is raining if we already know it is cloudy outside is an example of conditional probability.

Answer

Brief Explanations:

Conditional probability $P(A|B)$ is the probability of event $A$ occurring given that event $B$ has occurred. The probability of $A$ alone is just $P(A)$, not conditional. The probability that both $A$ and $B$ occur is $P(A\cap B)$. A simple probability like it is raining is not conditional. The probability that it is both raining and cloudy is $P(\text{rain}\cap\text{cloudy})$. But the probability that it is raining if we know it is cloudy is a conditional probability as it is probability of rain given cloudiness.

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.