A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones. 150 customers prefer the Cranberry Walnut Scones. 81 customers who responded were males and prefer the Chocolate Chip Scones. 172 female customers responded. Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones.

1. 25.6%

2. 24.1%

3. 72.9%

4. 98.4%

Question

Demarion

Mathematics

27 November, 06:53

A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones. 150 customers prefer the Cranberry Walnut Scones. 81 customers who responded were males and prefer the Chocolate Chip Scones. 172 female customers responded. Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones.

1. 25.6%

2. 24.1%

3. 72.9%

4. 98.4%

+3

Answers (2)

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Timothy Church · Answer 1

3. 72.9%

Step-by-step explanation:

Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.

So, the probability P (M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:

P (M∪C) = P (M) + P (C) - P (M∩C)

Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:

P (M) = 145/317 = 0.4574

There are 167 customers that prefer chocolate chips Scones (317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:

P (C) = 167/317 = 0.5268

Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate chip scones is:

P (M∩C) = 81/317 = 0.2555

Therefore, P (M∪C) is equal to:

P (M∪C) = 0.4574 + 0.5268 - 0.2555

P (M∪C) = 0.7287

P (M∪C) = 72.9%

Pearl · Answer 2

3. 72.9%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.

There are 172 female customers and 317-172 = 145 male customers.

150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.

81 of those are male, so 167 - 81 = 86 are female.

So the total of desired outcomes is 86 + 145 = 231

Total outcomes:

317 total customers.

Probability:

231/317 = 0.729

So the correct answer is:

3. 72.9%