Honey goes to school by a car driven by his driver or uses his bicycle. Probability that he will use the car is `(3)/(7)`. What is the probability that he will use his bicycle for going to the school?

Options

A. `(1)/(7)`
B. `(6)/(7)`
C. `(4)/(7)`
D. `(5)/(7)`

Answer

To find the probability that Honey will use his bicycle to go to school, we can follow these steps:

### Step 1: Understand the total probability
The total probability of all possible outcomes must equal 1. In this case, the two possible outcomes are using the car or using the bicycle.

### Step 2: Define the probabilities
Let:
- \( P(\text{Car}) \) = Probability that Honey uses the car = \( \frac{3}{7} \)
- \( P(\text{Bicycle}) \) = Probability that Honey uses the bicycle

### Step 3: Set up the equation
According to the total probability rule:
\[ P(\text{Car}) + P(\text{Bicycle}) = 1 \]
Substituting the known value:
\[ \frac{3}{7} + P(\text{Bicycle}) = 1 \]

### Step 4: Solve for \( P(\text{Bicycle}) \)
To find \( P(\text{Bicycle}) \), we can rearrange the equation:
\[ P(\text{Bicycle}) = 1 - P(\text{Car}) \]
Substituting the value of \( P(\text{Car}) \):
\[ P(\text{Bicycle}) = 1 - \frac{3}{7} \]

### Step 5: Convert 1 to a fraction
To perform the subtraction, convert 1 into a fraction with a denominator of 7:
\[ 1 = \frac{7}{7} \]
Now substitute this into the equation:
\[ P(\text{Bicycle}) = \frac{7}{7} - \frac{3}{7} \]

### Step 6: Perform the subtraction
Now, subtract the fractions:
\[ P(\text{Bicycle}) = \frac{7 - 3}{7} = \frac{4}{7} \]

### Final Answer
Thus, the probability that Honey will use his bicycle to go to school is:
\[ \boxed{\frac{4}{7}} \]