Probability question

Question

Que. URN 1 contains 2 red and 4 Blue balls, urn 2 contains 10 red and 2 Blue Balls. if an URN is chosen at random and a ball is removed from the chosen urn, what is the probability that the selected ball is blue? that it is red?

Answer 1

take a weighted average: 1/2 chance of urn I with probability of red 2/6= 1/3

1/2 chance of urn II with probability 10/12 = 5/6

(1/2)(1/3+5/6) = (1/2)(7/6) = 7/12 chance of red, 5/12 chance of blue

about 58.3% chance of red, 41.7% chance of blue