1. Acme, Incorporated, has installed a coffee dispenser in the lunch room. The m
ID: 2931509 • Letter: 1
Question
1. Acme, Incorporated, has installed a coffee dispenser in the lunch room. The machine dispenses a container of caffeinated Jones Brand coffee for $3.00 and a container of decaffeinated Jones brand coffee for $4.00. The same machine dispenses a container of caffeinated KM Brand coffee for $4.50 and a container of decaffeinated KM brand coffee for $3.50. Thirty percent of the coffee sold is Jones and seventy percent is KM. Sixty percent of purchasers of Jones coffee buy caffeinated coffee, whereas seventy-five percent of purchasers of KM coffee buy caffeinated coffee a) What proportion of caffeinated-coffee purchasers buy Jones brand? b) What are the average (mean) amounts paid for caffeinated and decaffeinated coffees at this machine? N.B. The answer to this requires two numbers.Explanation / Answer
Caffeinated Jones -$3
DeCaffeinated Jones -$4
Caffeinated KM-$4.5
DeCaffeinated KM-$3.5
Jones 30% sold,60% caffinated
KM - 70% sold,75% caffeinated
a)
total caffeinated buyers = 0.3*0.6+0.7*0.75 = 0.705
P(Jones brand|caffineinated) = 0.18/0.705 = 0.255
b)
caffeinated = 3*0.3*0.6+4.5*0.7*0.75 = $2.9
de caffeinated = 4*0.3*0.7+3.5*0.7*0.25 = $1.45
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