Calculating the Probability of Independent Events

When dealing with the probability of independent events, we can calculate the probability of rolling a 6 on a die and getting tails on a coin flip separately. The probability of rolling a 6 on a standard six-sided die is $\frac{1}{6}$, and the probability of getting tails on a fair coin is $\frac{1}{2}$.

To find the probability of both events occurring, we multiply their individual probabilities:

[ P(\text{rolling a 6 and getting tails}) = P(\text{rolling a 6}) \times P(\text{getting tails}) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12} ]

Therefore, the probability of rolling a 6 and getting tails is $\frac{1}{12}$.