Answer: [tex]\dfrac{5}{12}[/tex]
Step-by-step explanation:
Given : Urn 1 contains 2 white and 4 black balls and urn 2 contains 4 white and 4 black balls.
Total balls in Urn 1 = 6
Total balls in Urn 2 = 8
Probability of drawing white ball from Urn 1 = P(W |Urn 1) = [tex]\dfrac{2}{6}[/tex]
Probability of drawing white ball from Urn 2 = P(W |Urn 2)= [tex]\dfrac{4}{8}[/tex]
Then probability that Urn1 is chosen =P(Urn 1)[tex]=\dfrac{1}{2}[/tex]
Similarly , P(Urn 2)[tex]=\dfrac{1}{2}[/tex]
By Law of total probability :
P(White)= P(W |Urn 1) x P(Urn 1) +P(W |Urn 2) x P(Urn 12)
[tex]=\dfrac{2}{6}\times\dfrac{1}{2}+\dfrac{4}{8}\times\dfrac{1}{2}=\dfrac{5}{12}[/tex]
Hence, the probability that it is a white ball = [tex]\dfrac{5}{12}[/tex]
