Exercise 2. The following is a simple experiment in which probabilities can be d
ID: 3247469 • 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(An B)? (D) What is P(B | A')? (E) What is P(B)?Explanation / Answer
a)P(A) =probability that black marble is selected from Urn 1 =4/7
b) P(B|A) =probabilty that black marble from Urn 2 ; given black marble from Urn 1 to Urn 2
=selecting black marble out of 3 from total 4 marbles =3/4
c)P(A nB) =probability that black marble from Urn 1 to Urn2 and black marble from Urn 2
=P(A)*P(B|A) =(4/7)*(3/4) =3/7
D) P(B|A') =probability that black marble from Urn 2 ; given white marble from Urn 1 to Urn 2
=selecting black marble out of 2 from total 4 marbles =2/4=1/2
E)P(B) =selecting black marble from urn 2 =P(A)*P(B|A)+P(A')*P(B|A')
=(4/7)*(3/4)+(3/7)*(2/4) =18/28 =9/14
please revert for any clarification needed.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.