In 2013 Survey USA interviewed a random sample of 500 North Carolina residents,

asking them whether they think widespread gun ownership protects

law abiding citizens from crime, or make society more dangerous.

58% of all respondents said it protects citizens.

67% of white respondents, 28% of black respondents, and 64% of

Hispanic respondents shared this view. Based on these we want to fill in the

blank in the following sentence.

Opinion on gun ownership and race ethnicity

are most likely, which of the following?

Complementary, mutually exclusive, independent, dependent, or disjoint.

These should all be terms that you're familiar with by now.

Let's take a look at what we're given.

We're given that the probability that a

randomly chosen resident believes that guns protect citizens

is 0.58.

We also know that if the resident is white, then this probability is 0.67.

Once again, we use this vertical line notation to say the probability

that somebody believes that guns protect citizens, given that they're white.

And that probability is 0.67.

If they're black, the probability is 0.28, and lastly, if the

resident is Hispanic, the probability that they

believe that guns protect citizens is 0.64.

Since the probabilities of thinking that guns

protect citizens vary greatly based on the

person's race or ethnicity, Opinion on gun

ownership and race ethnicity are most likely dependent.

So knowing somebody's ethnicity might actually give us useful

information about their opinion on guns, and therefore, we are saying

that the two variables are most likely dependent on each other.