4. (Sec. 2.4) A department store sells sport shirts in three sizes (small, mediu

Question

4. (Sec. 2.4) A department store sells sport shirts in three sizes (small, medium, large), three patterns (plaid, print, stripe) and two sleeve lengths (long, short). The tables below give the proportions of shirts sold in the various category combinations Math 360-1 Homework 2 Page 2 of2 Short-Sleeved Size Pattern Plaid Print |Stipe Small Medium Large Long-Sleeved Size Pattern Plaid Print Stripe Small Medium Large 04 08 03 02 .07 .12 07 05 08 03 .10 04 02 05 02 03 07 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? (d) What is the probability that the size of the next shirt sold is medium? (e) Given that the shirt just sold was a short-sleeved plaid, what is the probability that ts size was medium? (f) Given that the shirt just sold was a medium plaid, what is the probability that it was short sleeved? Long sleeved?

Explanation / Answer

Each answer with formula and calculation below. Write back in case you have doubts:

a. P(next shirt is a med, long sleeved print ) = .05

b. P(next shirt is a med, print)
= P(next shirt is a med, print longsleeved)+P(next shirt is a med, print short sleeved)
= .07+.05
= .12

c. P(next shirt is sh0rt sleeved)
= Sum of all probabilites of getting a short sleeved shirt
= .04+.02+.05+.08+.07+.12+.03+.07+.08
= .56

d. P(next shirt is med)
= Sum of all probabilites of medium shirts
= .08+.07+.12+.1+.05+.07
= .49

e. P(given shirtsleeved, size is med)
= (.08+.07+.12)/.56
= .482

f. P(given med , short) = prob of all medium plaid, short sleved/ prob of medium plaid
= .1/(.08+.1)
= .556

P(given med , long) = prob of all medium plaid, long sleved/ prob of medium plaid
= (.08)/(.08+.1)
= .444

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