a. "Chocolate" and "Adults" (whatever those mean) will be independent as long as
"Chocolate" has the marginal distribution given by the second column, with a total probability of
Meanwhile, the joint probability of "Chocolate" and "Adults" is given by the cell in the corresponding row/column, with
The probabilities match, so these events are indeed independent.
Parts (b) and (c) are checked similarly.
b. Yes;
c. Yes;