A department store sells beds and dressers. 20%of the store’s customers purchase

Question

A department store sells beds and dressers. 20%of the store’s customers purchase both a bed and a dresser.Of those that purchase at most one of the items, 90% purchaseneither. Of those that purchase exactly one of the items, 75%purchase a dresser.

a. Construct a probability table.

b. What proportion of people purchase neitheritem?

c. What proportion of people purchase exactly oneof the items?

d. Are the events "purchase at most one of theitems" and "purchase at least one of the items" independent? Why orwhy not?

Explanation / Answer

let B : The customer buys bed
D: The customer buys dresser.
Let there be 100 people(doesn't matter how many you assumefinally you get the right proportion)
Now given that 20 people purchase both B and D.
So 80 people purchase at most one. So of these 80 people 90% -90%*80 = 72 people don't purchase any thing.
so remaining 80-72 = 8 people purchase either B or D butnot both i.e. exactly one.
of these that purchase exactly one 75% = 75% *8 = 6 purchaseonly D.
therefore the probability table is as below.
P(BD) = 20 %
P(B ) = P(BD)+P(B alone) = 20%+2% =22%.
P(D) = P(BD)+P(D) = 20%+6% = 26.%
P(BUD)c = 72%.
b) % of people buying neither = P(BUD)c =72% (from above)
c) % of people buying exactly % (from above)
d) No. Purchasing at most one item and at least one item can'tbe independent because the set of people purchasing exactly oneitem is common to both. Hence any two events that have a set ofoutcomes in common can't be independent of each other.
Hope it helps. Feel free to ask for any clarifications.

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