Question

shown below are the top 6 soft drinks in the united states. an employee at a theater concession stand recorded the number of drinks sold on a saturday.

soft drink	number sold
diet coke	37
pepsi	14
dr pepper	11
mountain dew	7
sprite	6

based on the employee’s records, which two statements about the soft drinks are true?
a. it is twice as likely for a pepsi to be sold than a mountain dew.
b. it is equally as likely for a dr pepper to be sold than a mountain dew or sprite.
c. it is less likely for a mountain dew to be sold than a sprite.
d. it is more than 3 times as likely for a coca cola to be sold than a dr pepper.
e. it is more likely a coca cola will be sold than a diet coke.

Explanation:

Step 1: Analyze Option A

• Number of Pepsi sold: \(14\)
• Number of Mountain Dew sold: \(7\)
• Calculate the ratio: \(\frac{14}{7}=2\). So Pepsi is twice as likely to be sold as Mountain Dew. Option A is true.

Step 2: Analyze Option B

• Number of Dr Pepper sold: \(11\)
• Number of Mountain Dew + Sprite sold: \(7 + 6 = 13\)
• Since \(11

eq13\), Dr Pepper is not equally likely to be sold as Mountain Dew or Sprite. Option B is false.

Step 3: Analyze Option C

• Number of Mountain Dew sold: \(7\)
• Number of Sprite sold: \(6\)
• Since \(7>6\), Mountain Dew is more likely to be sold than Sprite. Option C is false.

Step 4: Analyze Option D

• Number of Coca Cola sold: \(36\)
• Number of Dr Pepper sold: \(11\)
• Calculate the ratio: \(\frac{36}{11}\approx3.27>3\). So Coca Cola is more than 3 times as likely to be sold as Dr Pepper. Option D is true.

Step 5: Analyze Option E

• Number of Coca Cola sold: \(36\)
• Number of Diet Coke sold: \(37\)
• Since \(36<37\), Coca Cola is less likely to be sold than Diet Coke. Option E is false.

Answer:

B. It is equally as likely for a Dr Pepper to be sold than a Mountain Dew or Sprite.
C. It is less likely for a Mountain Dew to be sold than a Sprite. (Wait, no, Mountain Dew sold is 7, Sprite is 6. Wait, correction: Let's re - evaluate each option:

First, let's list the number of each drink sold:

• Coca Cola: 36
• Diet Coke: 37
• Pepsi: 14
• Dr Pepper: 11
• Mountain Dew: 7
• Sprite: 6

Option A:

Pepsi sold = 14, Mountain Dew sold = 7. \(14\div7 = 2\), so Pepsi is twice as likely to be sold as Mountain Dew. This statement is true.

Option B:

Dr Pepper sold = 11, Mountain Dew + Sprite sold = \(7 + 6=13\). \(11
eq13\), so this statement is false. Wait, maybe I misread. Wait, "It is equally as likely for a Dr Pepper to be sold than a Mountain Dew or Sprite" – maybe it's "Dr Pepper" vs "Mountain Dew" or "Sprite" (i.e., comparing Dr Pepper to Mountain Dew and Dr Pepper to Sprite separately? No, the wording is "than a Mountain Dew or Sprite" – maybe total? Wait, no, let's check again.

Wait, maybe the intended comparison is Dr Pepper (11) vs Mountain Dew (7) and Dr Pepper (11) vs Sprite (6). 11 is not equal to 7 or 6. So this statement is false.

Option C:

Mountain Dew sold = 7, Sprite sold = 6. 7>6, so it is more likely for Mountain Dew to be sold than Sprite. So this statement is false.

Option D:

Coca Cola sold = 36, Dr Pepper sold = 11. \(36\div11\approx3.27>3\), so it is more than 3 times as likely for Coca Cola to be sold than Dr Pepper. This statement is true.

Option E:

Coca Cola sold = 36, Diet Coke sold = 37. 36 < 37, so it is less likely for Coca Cola to be sold than Diet Coke. So this statement is false.

Wait, the question says "which TWO statements about the soft drinks are true?". So the correct ones are A and D.

Wait, let's re - check:

Option A: Pepsi (14) vs Mountain Dew (7). 14 is twice 7. So A is true.

Option D: Coca Cola (36) vs Dr Pepper (11). \(36\div11\approx3.27\), which is more than 3. So D is true.

So the two true statements are A and D.