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?
See your previous post.
To find P(A and B), we need to calculate the probability of event A happening first, and then event B happening second.
Event A: Drawing a white marble on the first draw
There are a total of 13 marbles in the jar (5 red + 8 white). Thus, the probability of drawing a white marble on the first draw is 8/13.
Event B: Drawing a red marble on the second draw
Since we are drawing without replacement, after the first draw, we are left with 12 marbles in the jar, with 4 red marbles and 8 white marbles remaining. So, the probability of drawing a red marble on the second draw given that a white marble was drawn first is 4/12.
To find the probability of both events happening (A and B), we multiply the probabilities of the individual events:
P(A and B) = P(A) * P(B|A)
P(A and B) = (8/13) * (4/12)
Simplifying this expression:
P(A and B) = (2/13) * (1/3)
P(A and B) = 2/39
Therefore, the probability of drawing a white marble on the first draw and then drawing a red marble on the second draw is 2/39.