A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid, print, and stripe), and two sleeve lengths (long and short). The accompanying table gives the proportions of shirts sold in the various category combinations. Short-sleeved
Pattern
Size Pl Pr St
S 0.04 0.02 0.05
M 0.07 0.10 0.12
L 0.03 0.07 0.08
Long-sleeved
Pattern
Size Pl Pr St
S 0.03 0.02 0.03
M 0.06 0.07 0.07
L 0.04 0.02 0.08
(a) What is the probability that the next shirt sold is a medium, long-sleeved, print shirt?
(b) What is the probability that the next shirt sold is a medium print shirt?
(c) What is the probability that the next shirt sold is a short-sleeved shirt?
What is the probability that the next shirt sold is a long-sleeved shirt?
(d) What is the probability that the size of the next shirt sold is medium?
What is the probability that the pattern of the next shirt sold is a print?
(e) Given that the shirt just sold was a short-sleeved plaid, what is the probability that its size was medium?
(f) Given that the shirt just sold was a medium plaid, what is the probability that it was short-sleeved?
What is the probability that it was long-sleeved?
2.Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard where P(A) = 0.45 P(B) = 0.45, and P(A ? B) = 0.30. Calculate and interpret each of the following probabilities (a Venn diagram might help).
(b) P(B' | A)
(e) Given that the selected individual has at least one card, what is the probability that he or she has a Visa Card?