The following is a simple experiment in which probabilities can be determined us
ID: 3183079 • Letter: T
Question
The following is a simple experiment in which probabilities can be determined using conditional probabilities. This experiment begins with two. 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(B|A)? (C) What is P(A Intersection B)? (D) What is P{B|A')? (E) What is P(B)?Explanation / Answer
1) P(A)=5/7 (as 5 black ball out of 7)
2)P(B|A)=P(A&B)/P(A) =(5/7)*(2/3)/(5/7)=2/3 (As if black ball goes to B ; there are 2 black ball out of 3)
3)P(AnB)=(5/7)*(2/3) =10/21
4) P(B|A') =1/3 as there will be one black among 3 if white ball goes
5)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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