The following is a simple experiment in which probabilities can be determined us
ID: 3175408 • Letter: T
Question
The following is a simple experiment in which probabilities can be determined using conditional probabilities. This experiment begins with two urns. Urn #1 starts with 4 black marbles and 7 white marbles. Urn #2 starts with 3 black marbles and 2 white marbles. For purposes of selection, assume every marble in an urn is equally likely to be chosen. The experiment has two steps. First, a marble is chosen at random from Urn #1. The selected marble is added to Urn #2. Next, one of the (now 6) marbles in Urn #2 is selected. Let A be the event that the marble selected from Urn #1, and moved to Urn #2, is black. Let B be the event that the second selection, of a marble from Urn #2, is black. What is P(A)? What is P(B|A)? What is P(A intersection B)? What is P(B|A')? What is P(B)?Explanation / Answer
Urn #1 - 4 Black + 7 White
Urn #2 - 3 Black + 2 White
(A)
A is an event that the marble selected from urn #1 and moved to urn #2 is black.
P(A) = 4C1/11C1 = 4/11
(B)
When a black marble is selected from urn 1 and added to urn 2. There will be 4 black and 2 white marbles in urn 2.
Selecting a black marble from urn #2 can be done in 4C1 ways.
Hence P(B|A) = 4C1/6C1 = 4/6 = 2/3
(C)
P(A)*P(B|A) = P(A and B)
P(A and B) = 4/11*4/6 = 16/66 = 8/33
(D)
If A' happens, there will be 3 black and 3 white marbles in urn 2,
P(B|A') = 3/6 = 1/2
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