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 Pr 0.040.02 0.05 0.06 .08 0.12 0.07 Size P St 0.03 0.08 Long-sleeved Pattern Pr 0.02 0.10 0.06 0.07 0.04 0.02 0.08 Size PI St 0.03 0.03 (a) What is the probability that the next shirt sold is a medium, long-sleeved, print shirt? ) 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 ) 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 madium? (Round your answer to three decimal places.)

Explanation / Answer

from above:

a)

P(medium ; long sl;eeved ; print) =0.06

b)probability =0.08+0.06 =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) =0.17+0.1 =0.27

e)

P( medium|short sleeved plaid) =0.06/0.13 =0.462

short sleeved long sleeved pl pr st Total 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 0.08 0.12 0.26 M 0.1 0.06 0.07 0.23 L 0.03 0.07 0.08 0.18 L 0.04 0.02 0.08 0.14 Total 0.13 0.17 0.25 0.55 Total 0.17 0.1 0.18 0.45

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