20 percent of blue eyed people have brown hair and thirty percent of non blue eyed people have brown hair. 10 percent of people are blue eyed. A random person has brown hair. What is the probability that person has blue eyes.
0.2 BE have BH and 0.3 BE^C have BH P(BE) = 0.1 P(BE^C) = 0.9 P(BH|BE) = 0.2 P(BH|BE^c) = 0.3 P(BH) = P(BH|BE) + P(BH|BE^c) = 0.2 + 0.3 = 0.5
So P(BE|BH) = P(BH|BE)P(BE)/(P(BH)) = (0.2)(0.1)/(0.5) = 0.4. Is this correct?