You are trying to decide whether to buy Brand A or Brand B as your new dishwashe
ID: 3200132 • Letter: Y
Question
You are trying to decide whether to buy Brand A or Brand B as your new dishwasher. Each brand is expected to last about 10 years. Brand A has a price of $950 and comes with an unlimited number of repairs at $150 each. Brand B has a higher price, $1200, but comes with an unlimited number of free repairs. Which dishwasher you buy depends on the number of repairs you expect Brand A to require. You investigate and find out the information about Brand A in Display 6.22.
Number of repairs: 0, 1, 2, 3, 4
Probabilities: 0.40, 0.30, 0.15, 0.10, 0.05
a. Find the expected cost of each brand, including original price and repairs.
b. What would be the advantage of buying Brand A? Brand B?
Explanation / Answer
Answer:
You are trying to decide whether to buy Brand A or Brand B as your new dishwasher. Each brand is expected to last about 10 years. Brand A has a price of $950 and comes with an unlimited number of repairs at $150 each. Brand B has a higher price, $1200, but comes with an unlimited number of free repairs. Which dishwasher you buy depends on the number of repairs you expect Brand A to require. You investigate and find out the information about Brand A in Display 6.22.
Number of repairs: 0, 1, 2, 3, 4
Probabilities: 0.40, 0.30, 0.15, 0.10, 0.05
a. Find the expected cost of each brand, including original price and repairs.
x
p
x*p
0
0.4
0
1
0.3
0.3
2
0.15
0.3
3
0.1
0.3
4
0.05
0.2
total
1.1
Expected number of repairs = 1.1
Expected cost= price + repair cost
Expected cost for brand A = 950+1.1*150 = $1115
Expected cost for brand B = 1200+1.1*0 = $1200
b. What would be the advantage of buying Brand A? Brand B?
Buying Brand A would be advantage.
x
p
x*p
0
0.4
0
1
0.3
0.3
2
0.15
0.3
3
0.1
0.3
4
0.05
0.2
total
1.1
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