Question

1. Miele is a German manufacturer of high-end domestic appliances and commercial equipment. One of the Miele dealers sells three types of Miele portable vacuum cleaners: Miele Complete, Miele Compact, and Miele Classic. About 28% of the customers buy Miele Complete, 71% of which also purchase an extended warranty. 55% of the buyers prefer Miele Compact, and 89% of them purchase an extended warranty as well. Finally, 17% of the customers buy Miele Classic, and 93% of them also buy an extended warranty.

a. What is the probability that a customer buys a Miele Classic with the extended warranty?

b. What is the probability that a customer did not purchase an extended warranty?

2. In how many different ways can the letters of the word MANAGEMENT be arranged?

3. In a marketing survey of 200 people about headache r-fief options, 85 said they preferred Brand A, 72 said they preferred Brand B, and 27 said they preferred Brand C, while the remainder said they did not have any preferences and would typically purchase whichever brand was cheapest. What is the probability that a randomly selected participant does not have any preference about which brand of medication they choose for headache relief?

Answer 1

The probability a customer buys a Miele Classic with an extended warranty is 15.81%. The probability of not purchasing an extended warranty is 15.36%. There are 3,682,800 ways to arrange MANAGEMENT, and an 8% chance a surveyed individual has no headache medication brand preference.

Step-by-step explanation:

1. To find the probability that a customer buys a Miele Classic with the extended warranty, we multiply the probability of a customer choosing a Miele Classic by the probability that they also purchase an extended warranty for it: 17% * 93%, which yields 0.17 * 0.93 = 0.1581 or 15.81%.

For part b, we calculate the probability of not purchasing an extended warranty. We know:

• 28% buy Miele Complete, 71% of these also buy an extended warranty, therefore 29% do not.
• 55% buy Miele Compact, 89% of these also buy an extended warranty, therefore 11% do not.
• 17% buy Miele Classic, 93% of these also buy an extended warranty, therefore 7% do not.

Using these percentages, we multiply by the probabilities and sum up the results:

• 28% * 29% = 0.0812 or 8.12%
• 55% * 11% = 0.0605 or 6.05%
• 17% * 7% = 0.0119 or 1.19%

We then add these probabilities together to find the total probability of not purchasing an extended warranty:

8.12% + 6.05% + 1.19% = 15.36%

2. To determine the number of different ways to arrange the letters of the word MANAGEMENT, we count the letters (10 in total), noting that there are duplicate letters. Using the formula for permutations of a word with duplicate letters, we divide the factorial of the total number of letters by the factorial of each duplicate letter's occurrences:

Number of arrangements = ⁡10!⁡⁡/⁡(2! * 2! * 2!) = 3,682,800

3. For calculating the probability of not having any brand preference in the headache relief medication survey, we subtract the number of people with preferences from the total number surveyed:

Total without preference = 200 - (85 + 72 + 27) = 200 - 184 = 16

Therefore, the probability of having no preference is 16/200 or 8%.