If x denotes the number of sixes in four consecutive throws of a dice, then P(x=4) is

Options

A. `1/1296`
B. `4/6`
C. 1
D. `1295/1296`

Answer

To find the probability \( P(x = 4) \), where \( x \) denotes the number of sixes in four consecutive throws of a dice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the probability of rolling four sixes in four throws of a fair six-sided die.

2. **Determine the Sample Space**: When a single die is thrown, there are 6 possible outcomes (1, 2, 3, 4, 5, 6). For four throws, the total number of outcomes in the sample space is:
\[ 6^4 = 1296 \]

3. **Identify the Favorable Outcomes**: The only way to get exactly four sixes in four throws is to roll a six every time. This specific outcome is:
\[ (6, 6, 6, 6) \]
There is only **1 favorable outcome**.

4. **Calculate the Probability**: The probability \( P(x = 4) \) is given by the ratio of the number of favorable outcomes to the total number of outcomes in the sample space:
\[ P(x = 4) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{1296} \]

5. **Final Answer**: Therefore, the probability \( P(x = 4) \) is:
\[ P(x = 4) = \frac{1}{1296} \]