Exercise 2. The following is a simple experiment in which probabilities can be d
ID: 3260980 • Letter: E
Question
Exercise 2. 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 3 white marbles. Urn #2 starts with 2 black marbles and 1 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 4) 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.
(A) What is P(A)?
(B) What is P(B | A)?
(C) What is P(A B)?
(D) What is P(B | A0 )?
(E) What is P(B)?
Explanation / Answer
a) P(A)= Number of blacks in Urn 1 / Total Marbles in Urn 1 = 4/7 = 0.57143
b) P(B/A) = Number of blacks in Urn 2 / Total Marbles in Urn 2
= 3 / 4 = 0.75
c) P(A and B) = (4/7) * (3/4) = 0.4285725
d) P(B/Ac) = 2 / 4 = 0.5
e) P(B) = P(A) P(B/A) + P(Ac) P(B/Ac)
= 0.57143*0.75 + (1-0.57143)*0.5 = 0.6429
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