A jar contains 5 red marbles and 8 white marbles.

Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
If two marbles are drawn from the jar, one after the other without replacement, what is P(A and B) expressed in simplest form?

To find the probability of two events occurring in sequence, we need to determine the probability of each event and multiply them together.

First, let's calculate the probability of Event A, which is drawing a white marble on the first draw. There are a total of 13 marbles in the jar (5 red + 8 white), so the probability of drawing a white marble on the first draw is:

P(A) = (number of white marbles) / (total number of marbles)
P(A) = 8 / 13

Now, let's calculate the probability of Event B, which is drawing a red marble on the second draw. After the first draw, there are 12 marbles left in the jar (4 red + 8 white). Since one white marble has already been drawn, there are 4 red marbles remaining. Therefore, the probability of drawing a red marble on the second draw is:

P(B | A) = (number of red marbles) / (total number of remaining marbles)
P(B | A) = 4 / 12
P(B | A) = 1 / 3

Finally, we can calculate the probability of both events A and B occurring by multiplying their individual probabilities:

P(A and B) = P(A) * P(B | A)
P(A and B) = (8/13) * (1/3)
P(A and B) = 8/39

Therefore, the probability of drawing a white marble on the first draw and a red marble on the second draw is 8/39.

P(A&B) = P(A)*P(B) = 8/13 * 5/12 = _____