Question

Urn 1 contains 8 green balls and 10 red balls. Urn 2 contains 7 green balls and 5 red balls. A die is rolled, if a 1 or 2 is rolled, a ball is chosen from urn 1, if a 3, 4, 5, or 6 is rolled, a balls is chosen from urn 2. What is the probability of selecting a green ball? Please show all work.

Answer 1

urn 1 contains 8 green balls and 10 red balls .

urn 2 contains 7 green balls and 5 red balls .

a die is rolled . if result is 1 or 2 , a ball is chosen from urn 1 .

if result is 3,4,5, or 6 , a ball is chosen from urn 2 .

to find the probability of getting a green ball .

P(green ball)=P(green ball and from urn 1)+P(green ball and from urn 2)

=P(green ball given urn 1)P(urn 1 is chosen )+P(green ball given urn 2)P(urn 2 is chosen)

now, P(green ball given urn 1)

=8/18

=0.44

P(urn 1 is chosen)

=P(die gives 1 or 2)

=1/3

P(green ball given urn 2)

=7/12

0.5833

P(urn 2 is chosen )

=P(die gives 3,4,5 or 6 )

=2/3

so, probability of selecting a green ball is

=0.5833*(2/3)+0.44*(1/3)

=0.53555

the probability of selecting a green ball is