PROBLEM 4. A department store sells sport shirts in three sizes (small, medium,

Question

PROBLEM 4. A department store sells sport shirts in three sizes (small, medium, and large) and two sleeve lengths (long and short). The Contingency Table provides the proportions of shirts sold in the various category combinations. Answer the following questions. (Round up your answers to 2 decimal places) Medium 0.18 0.22 Small Large 0.20 0.14 Short-sleeved Long-sleeved 0.10 a. Find the probability that the next shirt sold is a small, shirt-sleeved shirt. Answer: b. Find the probability that the next shirt sold is a long-sleeved shirt. Answer: c. Let A-(next shirt sold is large and B (next shirt sold is long-sleeved Are A and B mutually exclusive? Prove your answer Answer: d. Find the probability that next shirt sold is large given that it is long-sleeved. Answer:

Explanation / Answer

P(small and short sleeved) = ?

a.Add up all probability , you should get a 1
x+.18+.20+.10+.22+.14 = 1
x = .16

b. P(next shirt sold is a long sleeved shirt) = .10+.22+.14 = 46

c. A and B would have been mutually exclusive if P(A and B) = 0. In this case it is not so, as P(A and B) = .14

d. P(next shirt is large| given it is long sleeved) = .14/(.14+.22+.10) = .3044

e. For A and B to be independent P(A and B) = P(A)*P(B) .

P(A and B) = .14, P(A) = .20+.14 = .34,

P(B) = = 0.1+.22+.14 = .36

Now, P(A)*P(B) = .34*.36 = .1224

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