There are 20 cards numbered from 1 to 20. One card is drawn at random. What is the probability that the number on this card is a multiple of 4 ?

Options

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

Answer

To find the probability that the number on a randomly drawn card is a multiple of 4, we can follow these steps:

### Step 1: Identify the total number of cards
The total number of cards is given as 20, numbered from 1 to 20.

**Hint:** The total number of outcomes in a probability problem is the total number of items or events possible.

### Step 2: Identify the favorable outcomes
Next, we need to find how many of these cards are multiples of 4. The multiples of 4 between 1 and 20 are:
- 4 (4 x 1)
- 8 (4 x 2)
- 12 (4 x 3)
- 16 (4 x 4)
- 20 (4 x 5)

So, the multiples of 4 in this range are 4, 8, 12, 16, and 20. This gives us a total of 5 favorable outcomes.

**Hint:** To find favorable outcomes, list all the numbers that meet the criteria (in this case, multiples of 4).

### Step 3: Calculate the probability
The probability (P) is calculated using the formula:

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

Substituting the values we have:

\[ P(\text{multiple of 4}) = \frac{5}{20} \]

### Step 4: Simplify the fraction
Now, we can simplify the fraction:

\[ P(\text{multiple of 4}) = \frac{5 \div 5}{20 \div 5} = \frac{1}{4} \]

### Final Answer
The probability that the number on the drawn card is a multiple of 4 is \(\frac{1}{4}\).

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