A department store sells sport shirts in three sizes (al, mediun, and large). th

Question

A department store sells sport shirts in three sizes (al, mediun, and large). threc patterns (plaid, print, and stripe) and two sleeve lengths (long and short). The accompanying tables give the proportions of shirts sold in the various categery combinations Patterm Pr 0.04 0.02 0.05 SicePI St M 0.05 0.05 0.12 0.03.7 0.0 Size Pl D.G20.03 0.00.12 0.0 0.04 0.02 0.00 (a) What is the probability that the next shirt sold is a medium, long sleeved, print shirt? what is the prohability 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 lona sleeved shirt? siort-sleeved shirt (d) What is the probability that the size of the next shirt sold is medium? What is the prabability that the patten 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 Given that the shirt ust sold was a medium plaid, what is the probo lity that it was short-sleeved? Long-see ed? Round your answer to three decimal places long-sleeved

Explanation / Answer

from above:

a)

probability =0.12

b)

probability =0.05+0.12 =0.17

c)

short sleeved shirt =0.51

long sleeved shirt =0.49

d)

probability that next shirt is medium =0.22+0.27 =0.49

probability that pattern of next shirt is print =0.14+0.16 =0.30

e)

P(medium|short sleeve) =0.05/0.12 =0.417

f)

probability of short sleeved =0.05/(0.05+0.08)=0.385

log sleeved =0.08/(0.05+0.08)=0.615

Short sleeve long sleeve 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 0.05 0.05 0.12 0.22 M 0.08 0.12 0.07 0.27 L 0.03 0.07 0.08 0.18 L 0.04 0.02 0.08 0.14 total 0.12 0.14 0.25 0.51 total 0.15 0.16 0.18 0.49

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