In a sports academy, there are 20 balls, including 5 footballs. What is the probability that a randomly selected ball will be a football ?

Options

A. `1/3`
B. `3/2`
C. `1/4`
D. 1

Answer

To find the probability that a randomly selected ball from a sports academy will be a football, we can follow these steps:

### Step 1: Identify the total number of balls
We know that there are a total of 20 balls in the sports academy.

### Step 2: Identify the number of favorable outcomes
Out of the 20 balls, there are 5 footballs. These are our favorable outcomes.

### Step 3: Use the probability formula
The probability \( P \) of an event is given by the formula:

\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

### Step 4: Substitute the values into the formula
Here, the number of favorable outcomes (football) is 5, and the total number of outcomes (total balls) is 20. So we can substitute these values into the formula:

\[ P = \frac{5}{20} \]

### Step 5: Simplify the fraction
Now, we can simplify the fraction:

\[ P = \frac{5 \div 5}{20 \div 5} = \frac{1}{4} \]

### Step 6: State the final probability
Thus, the probability that a randomly selected ball will be a football is:

\[ P = \frac{1}{4} \]

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