One in a hundred million people is a genius If they are a ge

One in a hundred million people is a genius. If they are a genius, the probability that the person is acting extremely quirky is 0.999. If someone is not a genius, the probability that they are acting extremely quirky is 0.01. Someone is acting quirky – what is the probability that they are a genius? A. 0.01 B. About 1 in 10000 C. 0 D. 0.999 E. About 1 in a million

Solution

Let

Q = quirky
G = genius

As

P(G|Q) = P(G) P(Q|G) / P(Q)

As

P(Q) = P(G) P(Q|G) + P(G\') P(Q|G\') = (1/100000000)*(0.999) + (1-1/100000000)*(0.01) = 0.01000001

Thus,

P(G|Q) = P(G) P(Q|G) / P(Q) = (1/100000000)*(0.999)/0.01000001

= 9.98999*10^-7 OR, ABOUT ONE IN A MILLTION [OPTION E]