A crate of soft drinks contains 10 bottle of Coca-Cola 8 of Fanta and 6 of Sprite. If one bottle is selected…

1. Analyze the question

We are given a total collection of bottles and asked to find the probability of picking a bottle that is not Coca-Cola. To solve this, we need the total number of bottles and the number of bottles that are either Fanta or Sprite.

2. Explain the concept

Probability is defined as:

When dealing with "Not" a specific item, you can use the Complementary Probability rule:

Alternatively, you can simply add up all the items that satisfy the condition "Not Coca-Cola."

3. Show the solution

Step 1: Find the total number of bottles.

• Coca-Cola = 10
• Fanta = 8
• Sprite = 6
• Total = $10 + 8 + 6 = 24$

Step 2: Find the number of bottles that are "Not Coca-Cola." These are the Fanta and Sprite bottles:

• Not Coca-Cola = $8 (\text{Fanta}) + 6 (\text{Sprite}) = 14$

Step 3: Calculate the probability.

Step 4: Simplify the fraction. Divide both the numerator and the denominator by their greatest common divisor, which is 2:

(Verification using the Complementary Rule: $P(\text{Coca-Cola}) = \frac{10}{24} = \frac{5}{12}$. Therefore, $P(\text{Not Coca-Cola}) = 1 - \frac{5}{12} = \frac{7}{12}$.)

4. Identify the answer

The calculated probability is $\frac{7}{12}$, which matches option D.

5. Tip

In probability questions, always check if it is easier to calculate the probability of the event happening or the probability of it not happening. If the "not" category has fewer items, calculate that directly. If the "not" category is larger, subtract the probability of the event from 1 to save time!