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11Alexandr11 [23.1K]
3 years ago
15

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
Mathematics
1 answer:
Mila [183]3 years ago
5 0

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: 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)=\frac{P(Q\cap G)}{P(Q)}

P(G|Q)=\frac{0.999\cdot0.00000001}{0.999\cdot0.00000001+0.01\cdot0.99999999}

P(G|Q)\approx 9.98999\times10^{-7}

Which is near about 1 in a million.

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

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