Question

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

Answer 1

The correct option is E) About 1 in a million.

Explanation:

Consider the provided information.

It is given that one in a hundred million people is a genius.

Let G represents the Genius and Q represents the quirky.

We need to find the probability that someone is acting quirky- what is the probability that they are a genius.

The probability that person is quirky is:
`P(Q)=0.999\cdot0.00000001+0.01\cdot0.99999999`

The probability of
`P(Q\cap G)=0.999\cdot0.00000001`

Hence, the required probability is:

`P(G|Q)=(P(Q\cap G))/(P(Q))`

`P(G|Q)=(0.999\cdot0.00000001)/(0.999\cdot0.00000001+0.01\cdot0.99999999)`

`P(G|Q)\approx 9.98999*10^(-7)`

Which is near about 1 in a million.

Hence, the correct option is E) About 1 in a million.