Hey!

Here's a problem I'm working on, was wondering whether you could help me with it

Jerry and Doris have abandoned their respective careers in education and puppy paw modeling and

have taken up new work as art curators. Doris has a keen eye for art and can spot a forgerythat is, identifies fake painting as fakewith probability 0.91, whereas Jerry is more easily fooled and only spots a fake painting as fake with probability 0.82. Doris and Jerry also are able to certify authentic art as authentic very well. When Doris sees an authentic modern art painting, she certifies it as authentic with probability 0.99. Jerry does the same thing, but

with probability 0.84.

Those working at SFMoMA are adamant that, based on past experience, the probability that each

painting they consider is authentic with probability 0.6. Assuming a single painting is fake, Jerry

and Doris independently identify that painting as fake. Similarly, Jerry and Doris independently

identify authentic paintings as authentic.

a. (5 points) Assuming a painting is authentic, what is the probability that neither Jerry nor Doris

believe it to be authentic?

b. (5 points) Assuming a painting is a forgery, what is the probability that exactly one of Doris

and Jerry identify it as a forgery?

c. (5 points) Given that both Doris and Jerry certify a painting as authentic, what is the probabil-

ity the painting is really a forgery?