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Answer:
37.21% probability that the person is a statistician.
Step-by-step explanation:
We have these following probabilities:
An 80% probability that a statistican is shy.
A 15% probability that an economist is shy.
At the gathering, a 90% probability that a person is an economist.
At the gathering, a 10% probability that a person is a statistican.
If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?
This can be formulated as the following question:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
So
What is the probability that the person is a statistican, given that he is shy?
P(B) is the probability of the person being a statistican. So P(B) = 0.1.
P(A/B) is the probability of a statistican being shy, so P(A/B) = 0.8.
P(A) is the probability of a person being a shy. This is 15% of 90%(economists) and 80% of 10%(statisticans). So
Finally
37.21% probability that the person is a statistician.