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.

(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?

(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? (Round your answer to three decimal places.)


(f) Given that the shirt just sold was a medium plaid, what is the probability that it was short-sleeved? Long-sleeved? (Round your answer to three decimal places.)

Short-sleeved Pattern Size Pl Pr St S 0.04 0.02 0.05 M 0.07 0.07 0.12 L 0.03 0.07 0.08

Explanation / Answer

a) P(Medium, long sleeved, print shirt) = 0.07

b) P(Medium, print shirt) = 0.07 + 0.07 = 0.14

c) P(Short sleeved shirt) = 0.55

P(Long Sleeved shirt) = 0.45

d) P(Medium) = 0.26 + 0.23 = 0.49

P(Print) = 0.16 + 0.11 = 0.27

e) P(Medium|Short sleeved plaid) = 0.07/(0.04 + 0.07 + 0.03) = 0.50

f) P(Short sleeved| Medium plaid) = 0.07/(0.07 + 0.09) = 7/16 = 0.438

P(Long sleeved| medium plaid) = 0.09/(0.07 + 0.09) = 9/16 = 0.562

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