Question

You roll a 6-sided dice two times what is the probability of rolling a number less than 4 and then rolling a 6

Answer 1

To find the probability of rolling a number less than 4 on the first roll and then rolling a 6 on the second roll with a 6-sided die, we can break this down into the following steps:

1. **Determine the outcome for the first roll:**
The numbers less than 4 on a 6-sided die are 1, 2, and 3. There are 3 favorable outcomes (1, 2, and 3) out of 6 possible outcomes.

\[
P(\text{first roll} < 4) = \frac{3}{6} = \frac{1}{2}
\]

2. **Determine the outcome for the second roll:**
There is only 1 favorable outcome for rolling a 6 out of 6 possible outcomes.

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

3. **Combine the probabilities:**
Since the two rolls are independent events, we multiply the probabilities of the two events.

\[
P(\text{first roll} < 4 \text{ and second roll} = 6) = P(\text{first roll} < 4) \times P(\text{second roll} = 6)
\]

Substituting the probabilities we found:

\[
P(\text{first roll} < 4 \text{ and second roll} = 6) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]

Thus, the probability of rolling a number less than 4 on the first roll and then rolling a 6 on the second roll is \(\frac{1}{12}\).