In a simultaneous throw of a pair of dice, find the probability of getting:
a doublet of even numbers.

Answer

To solve the problem of finding the probability of getting a doublet of even numbers when throwing a pair of dice, we can follow these steps:

### Step 1: Identify the Sample Space
When throwing two dice, each die has 6 faces, which means there are a total of \(6 \times 6 = 36\) possible outcomes when both dice are thrown. This is our total sample space.

**Hint:** Remember that the total outcomes when throwing two dice is the product of the outcomes of each die.

### Step 2: Identify the Favorable Outcomes
A doublet means that both dice show the same number. The even numbers on a die are 2, 4, and 6. Therefore, the possible doublets of even numbers are:
- (2, 2)
- (4, 4)
- (6, 6)

This gives us a total of 3 favorable outcomes.

**Hint:** List out the even numbers on a die and remember that a doublet means both dice must show the same number.

### Step 3: Calculate the Probability
The probability \(P\) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
Substituting the values we found:
\[ P(\text{Doublet of Even Numbers}) = \frac{3}{36} \]

### Step 4: Simplify the Probability
Now we simplify the fraction:
\[ P(\text{Doublet of Even Numbers}) = \frac{1}{12} \]

### Final Answer
The probability of getting a doublet of even numbers when throwing a pair of dice is \(\frac{1}{12}\).

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