Final answer:
The question about cookie containers lacks necessary information, but various examples show how to calculate cookie selection probabilities and jelly bean probabilities based on provided quantities. Probabilities are not independent when the outcome of one event influences the possible outcomes of another, as shown in the cookie example.
Step-by-step explanation:
The original question seems to be about determining the number of containers needed to evenly distribute cookies, but the information provided does not give the total number of cookies or the specific number of cookies per container, hence we cannot answer it directly. Instead, let's address the sample question about the cookie selection.
a. Drawing a tree diagram would involve two levels of branches. The first branch would be for the first cookie selection, splitting into two possibilities: chocolate (3 chances out of 10) and butter (7 chances out of 10). The second branch depends on the first choice. If a chocolate cookie is taken first, the second branch for chocolate would have 2 chances out of 9, and butter would have 7 out of 9. If a butter cookie is taken first, then the second branch for chocolate would have 3 out of 9 chances, and butter would have 6 out of 9.
b. The probabilities for the flavor of the second cookie that Miguel selects are not independent of his first selection because the outcome of the first draw affects the composition of the cookies remaining, thus affecting the probabilities for the second draw.
As for the jelly bean problem, probabilities P(B), P(G), P(O), P(P), P(R), and P(Y) represent the probability of selecting a jelly bean of a particular color from the jar. These probabilities could be calculated by dividing the number of jelly beans of each color by the total number of jelly beans in the jar. For instance, to find P(B), the probability of getting a blue jelly bean, we would divide the number of blue jelly beans by the total number in the jar:
P(B) = Number of blue jelly beans / Total number of jelly beans = 26 / 150