1. can you please provide a thorough explanation?

8 points) You are an art expert. You decide that you want to test your skills so you have the Gallery director bring out 10 real paintings and 10 forgeries. You then have them randomly select 15 of these paintings for analysis. (a) If we let X be the number of real paintings in the selection, what is the probability mass function of X? (3 points) (b) What is the probability that all paintings of one type are in the selection? (2 points) (c) What is the probability that the number of real paintings selected is within one stan- dard deviation of the expected number of real paintings? (3 points)