A department store sells sport shirts in three sizes (small, medium and large) a

Question

A department store sells sport shirts in three sizes (small, medium and
large) and three patterns (plaid, print and stripe). The accompanying incomplete table was
given to us that present the proportion of shirts sold in the various category combinations.
Plaid Print Stripe
Small 0.07 0.04 0.08
Medium 0.18 0.19
Large 0.09 0.16
(a) It turns out that the probability of ?nding a large shirt in this store given that the
customer wants a printed shirt is 0.36. Complete the joint probability table.
(b) Given that the shirt just sold was stripe, what is the probability that it was medium?
(c) Construct a tree diagram corresponding to the joint probability table.

Explanation / Answer

given that the probability of large given printed is 0.36, this becomes p(L|Pr)=0.36

(0.09)/(0.13+x)=0.36

0.09=0.0468+0.36x

0.09-0.0468=0.36x

x=0.0432/0.36=0.12

--fill in the remaining blank spaces by algebra. note: the sum of everything on the horizontal row should equal 1 and the sum of everything on the vertical column should also equal one.

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