A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles.
Event A = drawing a brown marble on the first draw
Event B = drawing an orange marble on the second draw
If two marbles are drawn from the jar, one after the other and not replaced, what is P(B|A) expressed in simplest form?
A.) 5/14
B.) 5/13
C.) 3/7
D.) 6/13
The Answer is D
D.) 6/13
To find P(B|A), we need to find the probability of drawing an orange marble, given that the first marble drawn was brown.
The probability of drawing a brown marble on the first draw is P(A) = 6/14, because there are 6 brown marbles out of a total of 14 marbles.
After drawing a brown marble on the first draw, there are now 13 marbles left in the jar, with 5 orange marbles.
The probability of drawing an orange marble on the second draw, given that the first marble drawn was brown, is P(B|A) = 5/13.
Therefore, the answer is B.) 5/13.
To find the probability of event B given that event A has already occurred (P(B|A)), we need to consider the number of favorable outcomes for event B after event A has occurred, and divide it by the total number of possible outcomes.
First, let's determine the number of favorable outcomes for event B given that event A has occurred. Since event A is drawing a brown marble on the first draw, we know that after event A, there are 5 orange marbles left in the jar.
Next, let's determine the total number of possible outcomes for event B. After drawing a brown marble on the first draw, we have a total of 13 marbles left in the jar (3 black marbles + 5 orange marbles + 5 brown marbles).
Therefore, the probability of event B given that event A has occurred is: P(B|A) = favorable outcomes / total outcomes = 5/13.
So, the answer is D.) 6/13.