Question

A department store se s sport shirts in three sizes small, medium, and large), three patterns i plaid, arins, 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 PI Pr S 0.04 0.02 M 0.09 0.07 L 0.03 0.07 St 0.05 0.12 0.08 Long-sleeved Pattern Size PI Prs t S 0.03 0.02 0.03 M 0.07 0.07 0.07 L 0.04 0.02 0.00 (a) What is the probability that the next shiit sold is a medium, long sleeved, print shirt? (by What is the probability trial the next sinirl sold is a mediuni print strin? 14 (c) Whet is the probability that the next shirt sold is a short-sleeved shirt? A long-sleeved shirt? short- cover shirt 57 long-sleeved shirt 13 (d) what is the probability that the size of the next shit sold is medium? What is the probebility thet 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 thet its size was medium? (Round your answer to three decimal plecus.) 500 (F) Given that the shirt just sold was a medium pleid, whet is the probability that it wes short-sleeved? Lorig-sleeved? Round your answer to three decimal places. short sleeved 571 long sleeved

Answer 1

short sleeve:						long sleeved						total
	pattern						pattern						pattern
size	Pl	Pr	St	total		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		S	0.07	0.04	0.08	0.19
M	0.09	0.07	0.12	0.28		M	0.07	0.07	0.07	0.21		M	0.16	0.14	0.19	0.49
L	0.03	0.07	0.08	0.18		L	0.04	0.02	0.08	0.14		L	0.07	0.09	0.16	0.32
total	0.16	0.16	0.25	0.57		total	0.14	0.11	0.18	0.43		total	0.3	0.27	0.43	1

e)P(medium|short sleeved plaid)=

0.09/0.16=

0.563

f)P(short sleeved|medium plaid)=				0.09/0.16=	0.563
P(long sleeved|medium plaid)=				0.07/0.16=	0.438