Exercise 2. The following is a simple experiment in which probabilities can be d
ID: 2931502 • Letter: E
Question
Exercise 2. The following is a simple experiment in which probabilities can be determined using oonditional 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 marble. 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 tlack. Let B be the event that the second selection, of a marble fron Urn #2. ix black. (A) What is P(A)? B) What is P(B | A)? (C) What is P(AnB)? (D) What is P(B | A? (E) What is P(B)?Explanation / Answer
A) P(A) =selected marble from Urn #1 is black =4/7 (as tere are 4 marbles out of 7)
B) P(B|A) =P( selected marble from Urn #2 is black given selected marble from Urn #1 was black)
=3/4 (as there will be 4 marbles out of which 3 will be black if selected marble from Urn #1 was black)
c) P(AnB)=P(selected marble from Urn #1 is black & selected marble from Urn #2 is black)
=(4/7)*(3/4) =3/7
d) P(B|A') =2/4 =1/2 (as there will be 2 black marble and 2 white marbles if selected marble from Urn #1 was not black)
e) P(B)= P(A)*P(B|A)+P(A')*P(B|A') =(4/7)*(3/4)+(3/7)*(2/4) =9/14
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