Answer:
The correct option is E) About 1 in a million.
Step-by-step 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: [tex]P(Q)=0.999\cdot0.00000001+0.01\cdot0.99999999[/tex]
The probability of [tex]P(Q\cap G)=0.999\cdot0.00000001[/tex]
Hence, the required probability is:
[tex]P(G|Q)=\frac{P(Q\cap G)}{P(Q)}[/tex]
[tex]P(G|Q)=\frac{0.999\cdot0.00000001}{0.999\cdot0.00000001+0.01\cdot0.99999999}[/tex]
[tex]P(G|Q)\approx 9.98999\times10^{-7}[/tex]
Which is near about 1 in a million.
Hence, the correct option is E) About 1 in a million.
