At Middle School, 3 out of 5 students make honor roll. What is the probability (in %) that a student does not make honor roll?

Options

A. 0.65
B. 0.4
C. 0.6
D. None of these

Answer

To solve the problem of finding the probability that a student does not make the honor roll, we can follow these steps:

### Step 1: Understand the given information
We know that 3 out of 5 students make the honor roll. This means that the probability of a student making the honor roll is given by:
\[ P(\text{Honor Roll}) = \frac{3}{5} \]

### Step 2: Use the complementary probability
The probability of an event not occurring can be found using the formula:
\[ P(\text{Not Honor Roll}) = 1 - P(\text{Honor Roll}) \]

### Step 3: Substitute the known values
Now, we can substitute the probability of making the honor roll into the formula:
\[ P(\text{Not Honor Roll}) = 1 - \frac{3}{5} \]

### Step 4: Calculate the probability
To perform the calculation:
1. Convert 1 into a fraction with the same denominator:
\[ 1 = \frac{5}{5} \]
2. Now, subtract:
\[ P(\text{Not Honor Roll}) = \frac{5}{5} - \frac{3}{5} = \frac{2}{5} \]

### Step 5: Convert the fraction to percentage
To express the probability as a percentage, we multiply the fraction by 100:
\[ P(\text{Not Honor Roll}) = \frac{2}{5} \times 100 = 40\% \]

### Final Answer
The probability that a student does not make the honor roll is **40%**.

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