Your local art museum has planned next year’s 52-week calendar by scheduling a mixture of 1-week and 2-week shows that feature the works of 22 painters and 20 sculptors. There is a showing scheduled for every week of the year, and only one artist is featured at a time. There are 42 different shows scheduled for next year. You have randomly selected one week to attend and have been told the probability of it being a 2-week show of sculpture is 3/13.

a. What is the probability that the show you have selected is a painter’s showing?

b. What is the probability that the show you have selected is a sculptor’s showing?

c. What is the probability that the show you have selected is a 1-week show?

d. What is the probability that the show you have selected is a 2-week show?