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03 Aug 2026, 10:45
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A vending machine dispenses one drink at random from 48 drinks stocked inside. Each drink is either Coke or Pepsi, and each drink is either bottled or canned. What is the positive difference between the probability that the drink dispensed is a canned Pepsi and the probability that the drink dispensed is a bottled Coke?
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
(2) 9 of the drinks are bottled Pepsi.
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
(2) 9 of the drinks are bottled Pepsi.
03 Aug 2026, 10:45
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Official Solution:
A vending machine dispenses one drink at random from 48 drinks stocked inside. Each drink is either Coke or Pepsi, and each drink is either bottled or canned. What is the positive difference between the probability that the drink dispensed is a canned Pepsi and the probability that the drink dispensed is a bottled Coke?
The question asks to find the value of \(\left|\frac{y}{48} - \frac{x}{48}\right| = \frac{|y - x|}{48}\). So, essentially, all we need to find is the value of \(y - x\).
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
This gives:
So, we have that \(y = x - 4\). Therefore, \(y - x = (x - 4) - x = -4\) and the positive difference is thus \(\frac{4}{48}\). Sufficient.
(2) 9 of the drinks are bottled Pepsi.
This gives:
That is not enough to determine \(y - x\). Not sufficient.
Answer: A
A vending machine dispenses one drink at random from 48 drinks stocked inside. Each drink is either Coke or Pepsi, and each drink is either bottled or canned. What is the positive difference between the probability that the drink dispensed is a canned Pepsi and the probability that the drink dispensed is a bottled Coke?
| Coke | Pepsi | TOTAL | |
|---|---|---|---|
| Bottled | \(x\) | ||
| Canned | \(y\) | ||
| TOTAL | 48 |
The question asks to find the value of \(\left|\frac{y}{48} - \frac{x}{48}\right| = \frac{|y - x|}{48}\). So, essentially, all we need to find is the value of \(y - x\).
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
This gives:
| Coke | Pepsi | TOTAL | |
|---|---|---|---|
| Bottled | \(x\) | \(= 24 - x\) | 24 |
| Canned | \(y = 20 - (24 - x) = x - 4\) | \(= 48 - 24 = 24\) | |
| TOTAL | 28 | \(= 48 - 28 = 20\) | 48 |
So, we have that \(y = x - 4\). Therefore, \(y - x = (x - 4) - x = -4\) and the positive difference is thus \(\frac{4}{48}\). Sufficient.
(2) 9 of the drinks are bottled Pepsi.
This gives:
| Coke | Pepsi | TOTAL | |
|---|---|---|---|
| Bottled | \(x\) | 9 | |
| Canned | \(y\) | ||
| TOTAL | 48 |
That is not enough to determine \(y - x\). Not sufficient.
Answer: A
