You are tossing a coin and rolling a number cube. What is the probability of obtaining tails and rolling a 3? Enter your answer as a fraction.

Answer 1

To determine the probability of obtaining tails when tossing a coin and rolling a 3 on a number cube (which is a fair six-sided die), we will calculate the probabilities of each event separately and then multiply them together since these two events are independent.

1. Probability of tossing tails: A coin has two sides (heads and tails), so the probability of getting tails is:

   $$P(\text{tails})=\frac{1}{2}$$

2. Probability of rolling a 3 on a number cube: A standard number cube has six faces, numbered from 1 to 6. The probability of rolling any specific number (including 3) is:

   $$P(\text{rolling a 3})=\frac{1}{6}$$

3. Combined Probability: Since these two events are independent, we can multiply their probabilities:

   $$P(\text{tails and rolling a 3})=P(\text{tails})\times P(\text{rolling a 3})=\frac{1}{2}\times \frac{1}{6}=\frac{1}{12}$$

Thus, the probability of obtaining tails and rolling a 3 is

$$\boxed{{\displaystyle \frac{1}{12}}}$$