# Bayesian probability question and conditional probability based on falsehoods

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!

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