A department store sells sport shirts in three sizes (small, medium, and large),

Question

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 0.04 0.02 0.05 M 0.08 0.07 0.12 0.03 0.07 0.08 Long-sleeved Pattern Size PI Pr St 0.03 0.02 0.03 0.09 0.06 0.07 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? A long-sleeved shirt? short-sleeved shirt 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?

Explanation / Answer

a) probability that next shirt is a medium ,long-sleeved and print shirt

= 0.06

b) probability that next shirt sold is a medium print shirt

= 0.06 + 0.07 = 0.13

c) short sleeved shirt = sum of all probability in 1st table = 0.56

long sleeved shirt = 1- 0.56 = 0.44

d)

probability that size of the next shirt is medium = 0.08+ 0.07+0.12 +0.09+0.06+0.07 = 0.49

probability that shirt sold is print = 0.02+0.07+0.07 +0.02+0.06+0.02 = 0.26

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