Questions: A single die is rolled twice. Find the probability of rolling a 1 the first time and a 4 the second time.

Solution Steps

To find the probability of rolling a 1 on the first roll and a 4 on the second roll with a single die, we need to consider the independent probabilities of each event. The probability of rolling a specific number on a fair six-sided die is 1/6. Since the rolls are independent, the combined probability is the product of the individual probabilities.

The probability of rolling a 1 on a fair six-sided die is given by:

\[ P(1) = \frac{1}{6} \]

Similarly, the probability of rolling a 4 is:

\[ P(4) = \frac{1}{6} \]

Since the two rolls are independent events, the combined probability of rolling a 1 on the first roll and a 4 on the second roll is the product of the individual probabilities:

\[ P(1 \text{ and } 4) = P(1) \times P(4) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]

In decimal form, this is approximately:

\[ P(1 \text{ and } 4) \approx 0.0278 \]

Final Answer