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 table gives the proportions of shirts sold in the various category combinations.

(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?


What is the probability that the next shirt sold is a 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?


(f) Given that the shirt just sold was a medium plaid, what is the probability that it was short-sleeved?


What is the probability that it was long-sleeved?

Short-sleeved Pattern Size Pl Pr St S 0.04 0.02 0.05 M 0.05 0.07 0.12 L 0.03 0.07 0.08 Long-sleeved Pattern Size Pl Pr St S 0.03 0.02 0.03 M 0.08 0.1 0.07 L 0.04 0.02 0.08

Explanation / Answer

from above table

a)  probability that the next shirt sold is a medium, long-sleeved, print shirt =0.1 (look in long sleeved table )

b)probability that the next shirt sold is a medium print shirt =0.07+0.1=0.17 (add up of medium shirt prob. from both tables

c)probability that the next shirt sold is a short-sleeved shirt =0.53

probability that the next shirt sold is a long-sleeved shirt=0.47

d)probability that the size of the next shirt sold is medium =0.24+0.25=0.49

e) probability that its size was medium, given shirt just sold was a short-sleeved plaid=0.24/0.53=0.45283

f)probability that it was short-sleeved ; given  shirt just sold was a medium plaid=0.05/(0.05+0.08)=0.3846

probability that it was long-sleeved ; given  shirt just sold was a medium plaid=0.08/(0.05+0.08)=0.615385

Short-sleeved Long-sleeved 5 Pattern Pattern 6 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 M 0.05 0.07 0.12 0.24 M 0.08 0.1 0.07 0.25 L 0.03 0.07 0.08 0.18 L 0.04 0.02 0.08 0.14 total 0.12 0.16 0.25 0.53 total 0.15 0.14 0.18 0.47

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.