In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize ?

Options

A. `10//35`
B. `25//35`
C. `15//35`
D. None of these

Answer

To find the probability of getting a prize in the lottery, we can follow these steps:

### Step 1: Identify the total number of outcomes
In the lottery, there are two types of outcomes: prizes and blanks. We have:
- Number of prizes = 10
- Number of blanks = 25

Total outcomes = Number of prizes + Number of blanks
Total outcomes = 10 + 25 = 35

### Step 2: Identify the number of favorable outcomes
The favorable outcomes for getting a prize are simply the number of prizes available, which is:
- Number of favorable outcomes = Number of prizes = 10

### Step 3: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ \text{Probability of getting a prize} = \frac{10}{35} \]

### Step 4: Simplify the fraction
To simplify the fraction \( \frac{10}{35} \):
- Both 10 and 35 can be divided by 5.
- \( \frac{10 \div 5}{35 \div 5} = \frac{2}{7} \)

### Final Answer
The probability of getting a prize in the lottery is \( \frac{2}{7} \).

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