Question

In: Statistics and Probability

A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid,...

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
Size Pl Pr St
S 0.04 0.02 0.05
M 0.08 0.05 0.12
L 0.03 0.07 0.08
Long-sleeved
Pattern
Size Pl Pr St
S 0.03 0.02 0.03
M 0.06 0.11 0.07
L 0.04 0.02 0.08

(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?

short-sleeved shirt     
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     
long-sleeved

Solutions

Expert Solution

Answer:

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

= P( Long sleeved, Medium and print shirt) = 0.11

b) probability that the next shirt sold is a medium print shirt

= P( Medium , print and short sleeved) + P( Medium , print and Long sleeved)

= 0.11 + 0.05

= 0.16

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

= P( Short sleeved ) =0.11 +0.25 + 0.18 = 0.54

probability that the next shirt sold is a Long-sleeved shirt

= P( Lonf sleveed) = 0.08 + 0.24 + 0.14 = 0.46

d) probability that the size of the next shirt sold is medium

= P( Medium and short sleeved) + P( medium and long sleeved)

= 0.25 + 0.24

= 0.49

= 0.14 + 0.15

= 0.29

= 0.08 / 0.15

= 0.53

f)

P( Short sleeved | medium and plaid)= P( Short sleeved , medium and laid) / P( medium and plaid)

= 0.08 / [0.08+0.06]

= 0.08/0.14

= 0.571

P( Long sleeved | medium and plaid)= P( Long sleeved , medium and laid) / P( medium and plaid)

= 0.06/ [0.08+0.06]

= 0.06/0.14

= 0.428

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orchestra answered 2 years ago
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