Question: Suppose there is a room filled with urns of two types. Type I urns contain 5 blue balls and 5 red balls. Type II urns contain 2 red balls and 8 blue balls. There are 700 Type I urns and 300 Type II urns in the room. They are distributed randomly and look alike. An urn is selected at random from the room and a ball is drawn from it.
A) What is the probability that the urn is Type I?
So that will be: total type 1 urns/total urns $= 700/1000 = 0.7$
B) What is the probability that the ball drawn is red?
I'm confused with this part of the question. My answer is:
(type 1 red balls) $\times$ (type 2 red balls)
(5 red balls/10 total balls) $\times$ (2 red balls/10 total balls) $= 1/10$
Is $1/10$ the probability to draw a red ball correct?