Each of the marbles in a jar is

Stephen Mortensen

r + w + b = t, where r = number of red marbles, w = number of white marbles, b = number of blue marbles, and t = total marbles. In order to determine the probability of drawing a blue marble, we will need to determine the ratio of blue marbles to total marbles, or b/t.

In option (1), we learn that r = 8 and t = 24, so 8 + w + b = 24. We can't solve for b, however, nor can we find a ratio, because we still need more information on w.

(2) gives us the information that t/2 = w. We could write this as r + b = t - w, r + b = t - t/2, and r + b = t/2. This still doesn't give us enough information to find a proper ratio, however, because r, b, and t are still undetermined.

The combination of (1) and (2), though, does provide the answers we need. We know that r = 8 and t = 24, and that w = t/2 = 12. So, since we have all of our values except for b, we know that we have the necessary information to solve for b and find the probability, b/t.

If we want to carry it through and actually solve, 8 + 12 + b = 24, b = 24 - 20, b = 4, b/t = 4/24 = 1/6, or about 16.67% probability.

May 11, 2016 • Comment