4. Probability

Suppose events E and F are such that $P(E\cap F)$ = $P\left(E\right)$ $\times$ $P\left(F\right)$. Are the events E and F independent or dependent? Justify your answer.

If you flip a fair coin, what is the probability of getting heads? Express your answer as a percentage.

Which of the following best describes the difference between $\mathrm{univariate}$ data and $\mathrm{bivariate}$ data?

If an event has a probability of $\frac{3}{4}$, how likely is it to occur?

Which of the following is not a voluntary response sample?

A bag contains $12$ marbles numbered $1$ to $12$. If a marble is chosen at random, what is the probability that it is either shaded (suppose marbles numbered $2$, $4$, $6$, $8$, $10$, and $12$ are shaded) or is labeled with a multiple of $3$?

Suppose you are given the following data for two variables, $X$ and $Y$: $(1,2)$, $(2,4)$, $(3,6)$, $(4,8)$. What is the value of the sample correlation coefficient between $X$ and $Y$? Do not round your intermediate calculations.

Suppose a researcher wants to determine the average height of all students currently enrolled at a large university. Should the researcher collect data from a sample or from the entire population?

Given any two events $A$ and $B$, which of the following correctly expresses the probability of their union $P(A\cup B)$?

Given a table that lists the number of cars sold by a dealership each day, is the random variable representing the number of cars sold discrete or continuous?

Which of the following best describes the difference between a $\mathrm{census}$ and a $\mathrm{sampling}$ in statistics?

Suppose a standard deck contains cards that are either striped or solid, and either blue or red. If the probability that a card is striped is $\frac{1}{2}$ and the probability that a card is blue is $\frac{1}{4}$, and being striped and being blue are independent events, what is the probability that a randomly selected card is both striped and blue?

A racehorse wins $5$ of its first $7$ races. What is the ratio of the number of races won to the number of races lost?

Which two essential features are present in all statistically designed experiments?

In the context of probability, what does it mean when sampling is done without replacement?