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 tables give the proportions of shirts sold in the various category combinations. 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 shortsleeved shirt? A long-sleeved shirt? d. ?What is the probability that the size of the next shirt sold is medium? 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? Longsleeved?

Answer : Step 1 of 6 : Given, 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 tables give 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 0.08 0.07 0.12 L 0.03 0.07 0.08 Long sleeved Pattern Size Pl Pr St S 0.03 0.02 0.03 M 0.1 0.05 0.07 L 0.04 0.02 0.08 a) The claim is to find the probability that the next shirt sold is a medium, long-sleeved, print shirt. From the table we can clearly know that P(next shirt sold is a medium, long -sleeved , print shirt) = 0.05 Step 2 of 6 : b) The claim is to find the probability that the next shirt is a medium print shirt P(medium print shirt) = P( medium print long sleeve) + P( medium print short sleeve) = 0.05+0.07 = 0.12 Step 3 of 6 : c) The claim is to find the next shirt sold is a short sleeved shirt and long sleeved shirt P(short sleeved shirt) = 0.04+0.08+0.03+0.02+0.07+0.07+0.05+0.12+0.08 = 0.56 P(long sleeved shirt) = 1 - P(short sleeved shirt) = 1 - 0.56 = 0.44