The following is a simple experiment in which probabilities can be determined us
ID: 3183135 • 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 5 black marbles and 2 white marbles. Urn #2 starts with 1 black marble 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 3) 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(BA)? (C) What is P(A intersection B)? (D) What is P (BA')? (E) What is P(B)?Explanation / Answer
P(A)=5/7 ; 5 black out of 7
P(B|A) =2/3 if one black is shifted to urn 2, then there are 2 black in urn of 3 marbles
P(AnB) =5/7 *2/3 =10/21
P(B|A'') =1/3 as if first urn will give white ball then there will be 1 black in urn of 3 marbles
P(B) =P(A)*P(B|A)+P(A')*P(B|A') =(5/7)*(2/3)+(2/7)*(1/3)=12/21
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