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 Size PI 0.04 0.05 0.03 0.02 0.07 0.07 St 0.05 0.12 0.08 Long-sleeved Pattern Size PI 0.03 0.06 0.04 0.02 0.12 0.02 St 0.03 0.07 0.08 (a) What is the probability that the next shirt sold is a medium, long-sleeved, print shirt? 12 (b) What is the probability that the next shirt sold is a medium print shirt? 19 (c) What is the probability that the next shirt sold is a short-sleeved shirt? A long-sleeved shirt? short-sleeved shirt 53 long-sleeved shirt 47 (d) What is the probability that the size of the next shirt sold is medium? 49 What is the probability that the pattern of the next shirt sold is a print? 32 (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

Explanation / Answer

As I can see you have answered a few parts correctly, let me guide you with the remaining parts.

e. P( Medium | Short sleeved plaid) = P(Medium and short sleeved plaid) / P(Short sleeved plaid)

= 0.05 / (0.04 + 0.05 + 0.03)

= 5/12 = 0.42

f. P(Short sleeved | Medium plaid) = P(Short sleeved and medium plaid) / P(medium plaid)

= 0.05 / (0.05 + 0.06)

= 5/11 = 0.45

P(long sleeved | medium plaid) = 1 - P(short sleeved | medium plaid) = 1 - 0.45 = 0.55

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