There are 100 cards numbered from 1 to 100 in a box. If a card is drawn from the box and the probability of an event is `1/2,` then the number of favourable cases to the event is:

Options

A. 20
B. 25
C. 40
D. 50

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Total Outcomes
We have a box containing 100 cards numbered from 1 to 100. This means the total number of outcomes when drawing a card is 100.

**Hint:** Remember that the total outcomes are simply the total number of items in the sample space.

### Step 2: Set Up the Probability Formula
The probability of an event is defined as the number of favorable outcomes divided by the total number of outcomes. We can express this as:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

**Hint:** The formula for probability is crucial for finding the number of favorable outcomes.

### Step 3: Substitute the Known Values
We are given that the probability of the event is \( \frac{1}{2} \). Therefore, we can write:
\[ \frac{X}{100} = \frac{1}{2} \]
where \( X \) is the number of favorable outcomes.

**Hint:** Make sure to substitute the correct values into the probability formula.

### Step 4: Cross Multiply to Solve for X
To eliminate the fraction, we can cross-multiply:
\[ X \cdot 2 = 100 \cdot 1 \]
This simplifies to:
\[ 2X = 100 \]

**Hint:** Cross-multiplication is a useful technique to solve equations involving fractions.

### Step 5: Solve for X
Now, divide both sides of the equation by 2 to find \( X \):
\[ X = \frac{100}{2} \]
Calculating this gives:
\[ X = 50 \]

**Hint:** Always perform the arithmetic carefully to ensure accuracy.

### Conclusion
The number of favorable cases for the event is 50.

**Final Answer:** 50