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aalyn [17]
3 years ago
14

At an art exhibition there are 12 paintings of which 10 are original. A visitor selects a painting at random and before decides

to buy he asks the opinion of an expert about the authenticity of the painting. The expert is right in 9 out of 10 cases on average. Given that the expert decides the painting is authentic what is the probability it really is? If the expert decides the paining is a copy then the visitor returns it and chooses another one what is the probability that her second choice is an original?
Mathematics
1 answer:
Reika [66]3 years ago
8 0

Answer:

a) 0.8333

b) 0.75

c) 0.8181 or 0.9090

Step-by-step explanation:

a)

The probability the visitor selects an authentic painting is  

10/12 = 0.8333

b)

Since the opinion of the expert does not depend on your choice, the events are <em>independent</em>, so the probability that the expert says is authentic and it really is, is

0.8333*0.9 = 0.75

c)

If the expert decides the painting is a copy and it is not, then there are 11 paintings of which 9 are authentic, so the probability the visitor selects a new original painting is

9/11= 0.8181

If the expert decides the painting is a copy and it is, then there are 11 paintings of which 10 are authentic, so the probability the visitor selects a new original painting is

10/11= 0.9090

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