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 0.06 0.07 0.12 L 0.03 0.07 0.08

Explanation / Answer

a) probability that the next shirt sold is a medium, long-sleeved, print shirt =0.12

b)probability that the next shirt sold is a medium print shirt =0.07+0.12=0.19

c) probability that the next shirt sold is a short-sleeved shirt =0.54

probability that the next shirt sold is a long-sleeved shirt =0.46

d) probability that the size of the next shirt sold is medium =0.25+0.24=0.49

probability that the pattern of the next shirt sold is a print =0.16+0.16=0.32

e)probability that its size was medium; given short sleeve plaid=0.06/0.13=0.462

f)probability that it was short-sleeved ; given sold was medium plaid =0.06/(0.06+0.05)=0.545

probability that it was long-sleeved ; given sold was medium plaid =0.05/(0.06+0.05)=0.455

Short-sleeved Long-sleeved Pattern Pattern Size Pl Pr St Total Size Pl Pr St Total S 0.04 0.02 0.05 0.11 S 0.03 0.02 0.03 0.08 M 0.06 0.07 0.12 0.25 M 0.05 0.12 0.07 0.24 L 0.03 0.07 0.08 0.18 L 0.04 0.02 0.08 0.14 Total 0.13 0.16 0.25 0.54 Total 0.12 0.16 0.18 0.46

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