Question

An urn contains two marbles. One marble is white. The other marble could be white or black.

a) You will draw one marble. What is the probability it will be white?

b) You have drawn one marble and it was white. What is the probability that the marble still in the urn is black?

c) You have replaced the white marble back into the urn. You will draw a marble again. What is the probability that it will be white?

d) You have drawn a marble and again it was white. What is the probability that the marble still in the urn is black?

Answer 1

a)probability it will be white=P(1 marble is white and you picked white marble)+P(both are white and you picked white)=(1/2)*(1/2)+(1/2)*1=3/4

b)

P(1 marble is white| you picked white marble)=

P(1 marble is white and you picked white marble)'/P(you picked white)=(1/2)*(1/2)/(3/4)=1/3

c)

P(white again given first drawn was white)=P(white again|1 marble white)*P(1 marble white|first drawn was white)+P(white again|both marble white)*P(both marble white|first drawn was white)

=(1/2)*(1/3)+1*(2/3)=5/6

d)

P(1 marble is whie given both draw marble are white)=(1/2)*(1/3)/(5/6)=1/5