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I'm having trouble understanding how to compute (a), if it's not a Bayes theorem problem. Why bother telling me about $A$ and $A^C$ compliment in that case?

How does this help me compute parts (b) and (c)?

Thank you!

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Part a) is just the law of total probability:

$P(\text{actually seen Nessie}) = P(\text{actually seen Nessie}|A).P(A) + P(\text{actually seen Nessie}|A^c).P(A^c)$

$P(\text{actually seen Nessie}|A) = 1 $ since they always tell the truth

$P(\text{actually seen Nessie}|A^c) = 1/1000 $ since they always say that they see it, so it is the probabiltiy that Nessie is seen in a given day

$P(\text{actually seen Nessie}) = 1. 0.99 + 0.01 . 1/1000$

and from now on you use this probability for part c for example

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