[16 points] A department store sells sport shirts in three sizes (small, medium,

Question

[16 points] 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 table below gives the proportions of shirts sold in the various category combinations. Short-sleeved Long-sleeved Pattern Pattern Size Plaid Print Stripe S 004 0.02 0.05 M | 0.08-0.07 (0.12) L| 0.03 0.07) 0.08 Size Plaid Print Stripe S 0.03 002 0,03 M 0.10 0.05 0.07 L 1 0.04 0.03 0.08 (a) What is the probability that the next shirt sold is a medium Short-sleeved,striped shirt? 12 points] (b) What is the probability that the next shirt sold is a large print shirt? 2 points (c) What is the probability that the size of the next shirt sold is small212 points (d) What is the probability that the next shirt sold is a long-sleeved plaid shirt? [2 points (e) Given that the shirt just sold was short-sleeved, what is the probability that its size was medium? [4 points] (O What is the probability that the shirt just sold was short-sleeved, given that it was a large print shirt? [4 points]

Explanation / Answer

Ans:

a)P(medium,short sleeved,stripe print)=0.12

b)P(large print shirt)=0.07+0.02=0.09

c)P(small size)=0.04+0.02+0.05+0.03+0.02+0.03=0.19

d)P(long sleeved plaid shirt)=0.03+0.1+0.04=0.17

e)P(medium/short sleeved)=(0.08+0.07+0.12)/0.56=0.27/0.56=0.482

f)P(short sleeved/large print)=0.07/(0.07+0.02)=0.07/0.09=0.78

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