Question

what is the probability of flipping tails and rolling a five? write your answer as a fraction or a whole number. with fractions, use a slash ( / ) to separate the numerator and denominator.

Explanation:

Step1: Determine the probability of flipping tails

A coin has 2 possible outcomes (heads or tails). The probability of flipping tails is $\frac{1}{2}$ since there is 1 favorable outcome (tails) out of 2 total outcomes.

Step2: Determine the probability of rolling a five

A standard die has 6 possible outcomes (1, 2, 3, 4, 5, 6). The probability of rolling a five is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 5) out of 6 total outcomes.

Step3: Use the multiplication rule for independent events

When two events are independent (the outcome of flipping a coin does not affect the outcome of rolling a die and vice - versa), the probability of both events occurring is the product of their individual probabilities. So, $P(\text{tails and five})=P(\text{tails})\times P(\text{five})$. Substitute the values: $\frac{1}{2}\times\frac{1}{6}=\frac{1\times1}{2\times6}=\frac{1}{12}$.

Answer:

The probability is $\frac{1}{12}$, where the numerator is $1$ and the denominator is $12$.