Urn 1 contains 6 red balls and 2 black balls. Urn 2 contains 2 red balls and 2 black balls. Urn 3 contains 5 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the probability that it will be red.
+23246 Urn 1 has 6 red balls and 2 black balls (total = 8 balls)
-- the probability of drawing a red ball from this urn is 6/8.
Urn 2 has 2 red balls and 2 black balls (total = 4 balls)
-- the probability of drawing a red ball from this urn is 2/4.
Urn 3 has 5 red balls and 2 black balls (total = 7 balls)
-- the probability of drawing a red ball from this urn is 5/7.
Since an urn is selected at random, the probability of drawing each urn is 1/3.
To find the final probability of selecting a red ball: for each urn -- multiply the probability of drawing an urn
times the probability of drawing a red ball from that urn, and add these three answers together.
Total proability: (1/3)(6/8) + (1/3)(2/4) + (1/3)(5/7) = 0.655
