A jar contains 4 brown marbles and 9 yellow marbles.
Event A = drawing a yellow marble on the first draw
Event B = drawing a brown 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?
A. 4/39
B. 3/13
C. 1/3
D. 9/13
thank you all
To calculate the probability of both events A and B occurring, you need to multiply the probability of event A by the probability of event B, given that event A has already occurred.
The probability of drawing a yellow marble on the first draw (event A) can be calculated as:
P(A) = Number of yellow marbles / Total number of marbles in the jar
P(A) = 9 / (4 + 9) = 9/13
After drawing one marble without replacement, there will be 12 marbles left in the jar (4 brown and 8 yellow). The probability of drawing a brown marble on the second draw (event B), given that event A has already occurred, can be calculated as:
P(B|A) = Number of brown marbles remaining / Total number of marbles remaining
P(B|A) = 4 / (4 + 8) = 4/12 = 1/3
To find the probability of both A and B occurring (P(A and B)), multiply the probabilities:
P(A and B) = P(A) * P(B|A)
P(A and B) = (9/13) * (1/3) = 9/39 = 3/13
Therefore, the correct answer is B. 3/13.