4. Probability

In probability theory, the probability of event $a$ given event $b$, denoted as $P\left(a\right|b)$, is equal to which of the following expressions?

In a particular week, a train company recorded the following percentages for late arrivals: $27.6\%$, $38.2\%$, $40.0\%$, and $72.4\%$. If the correct percentage of trains that were late is $27.6\%$, which of the following is the correct value?

A spinner is divided into $8$ equal sections: $3$ are red, $2$ are blue, and $3$ are green. If the spinner is spun once, what is the probability that it will land on a red section?

If $X$ is a continuous random variable uniformly distributed on the interval $[0,4.5)$, what is the probability that $X<3$?

Which of the following pairs of events are mutually exclusive ($AB=\; 15$)?

Suppose you calculate the mean height of all students in a particular college. Is this value a parameter or a statistic?

If arrivals occur according to a $\mathrm{Poisson}$ distribution with an average of $1$ arrival every $20$ minutes, what is the probability that exactly $2$ arrivals occur in a $40$-minute period?

Which of the following represents a valid probability distribution?

Epidemiologists can attempt to deal with confounding in a study by all but which of the following?

Which of the following probability statements represents a cumulative probability?

For mutually exclusive events A and B, the joint probability $P(A\cap B)$ is:

In the context of probability, which statement best describes a $\mathrm{marginal}\mathrm{distribution}$ as compared to a $\mathrm{conditional}\mathrm{distribution}$?

In the context of basic probability and statistics, which two of the following are considered primary sources of data?

Suppose the probability that it rains on a given day is $0.3$. What is the probability that it does not rain on that day?

In the context of probability and statistics, primary data are —.