A coin is flipped and a die is rolled. Find the probability of getting a tail on the coin and a 3 on the die.Question 3Answera.1/2b.1/12c.1/6d.8/12

1. Break Down the Problem

We need to find the combined probability of two independent events:

• Flipping a coin and getting a tail.
• Rolling a die and getting a 3.

2. Relevant Concepts

• The probability of an event occurring can be calculated using the formula: $P(A \cap B) = P(A) \times P(B)$ where $P(A)$ is the probability of event A, and $P(B)$ is the probability of event B.

3. Analysis and Detail

1. Calculate the probability of flipping a tail (Event A) $P(\text{Tail}) = \frac{1}{2}$

2. Calculate the probability of rolling a 3 on the die (Event B) $P(\text{3 on die}) = \frac{1}{6}$

3. Combine the probabilities $P(\text{Tail and 3}) = P(\text{Tail}) \times P(\text{3 on die}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$

4. Verify and Summarize

The combined probability of getting a tail on the coin and a 3 on the die is confirmed through multiplication: $P(\text{Tail and 3}) = \frac{1}{12}$

Final Answer

The probability of getting a tail on the coin and a 3 on the die is $\frac{1}{12}$.

So, the correct answer is b. $\frac{1}{12}$.