Two friends were born in the year 1996. The probability that they have the same birth date is

Options

A. `(1)/(183)`
B. `(2)/(365)`
C. `(1)/(365)`
D. `(1)/(366)`

Answer

To find the probability that two friends born in the year 1996 have the same birth date, we can follow these steps:

### Step 1: Determine if 1996 is a leap year
To check if a year is a leap year, we can use the rule that a year is a leap year if it is divisible by 4.

- **Calculation**:
- 1996 ÷ 4 = 499 (which is an integer)

Since 1996 is divisible by 4, it is a leap year.

### Step 2: Identify the total number of days in 1996
Since 1996 is a leap year, it has 366 days.

### Step 3: Determine the total possible outcomes
The total possible outcomes for the birth dates of the two friends are the total number of days in the year, which is 366.

### Step 4: Determine the number of favorable outcomes
The number of favorable outcomes where both friends have the same birth date is 1 (they can only share one specific date).

### Step 5: Calculate the probability
The probability \( P \) that both friends have the same birth date can be calculated using the formula:

\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{366} \]

### Final Answer
Thus, the probability that both friends have the same birth date is \( \frac{1}{366} \).

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