The following is a simple experiment in which probabilities be determined using

Question

The following is a simple experiment in which probabilities 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(B|A)? (C) What is P(A Intersection B)? (D) What is P(B|A')? (E) What is P(B)?

Explanation / Answer

here P(A) =5/7 as there are 5 marbles outof 7

P(B|A) =2/3 where if black marble is taken out from urn 1 then we have 2 black marble out of 3

P(AnB) =(5/7)*(2/3) =10/21

P(B|A') = 1/3

P(B) =(5/7)*(2/3)+(2/7)*(1/3)=12/21

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