- #1
Tajeshwar
- 11
- 0
Homework Statement
An Urn contains two white marbles and one black marble. A marble is drawn from the Urn without replacement and put aside without my seeing it. Then a second marble is drawn, and it is white.
What is the probability that the unknown removed marble is white, and what is the probability that it is black?
p(the first marble is white∣the second marble is white)=1.0
p(the first marble is black∣the second marble is white)=0.0
p(the first marble is white∣the second marble is white)=0.6667
p(the first marble is black∣the second marble is white)=0.333
p(the first marble is white∣the second marble is white)=0.3333
p(the first marble is black∣the second marble is white)=0.6667
p (the first marble is white |the second marble is white) =.5
p(the first marble is black | the second marble is white) =.5
Homework Equations
The Attempt at a Solution
My attempt is as follows:
P(first black ("FB") |second white ("SW")) = P(SW|FB)*P(FB)/(P(SW|FB)*P(FB)+P(SW|FW)*P(FW))
Using Bayes theorem.
This gives me = (1/2)*(1/3)/(1/6+1/3) = 0.33
Did a similar logic for P(First White|Second White) and got .66
But I am getting this question wrong when I pick the following answer:
p(the first marble is white∣the second marble is white)=0.6667
p(the first marble is black∣the second marble is white)=0.333