A coin and a die are thrown simultaneously. The probability that a head appears on coin and '3' on the die is

Options

A. `1//8`
B. `1//12`
C. `1//2`
D. 1

Answer

To solve the problem of finding the probability that a head appears on a coin and a '3' appears on a die when both are thrown simultaneously, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Events**:
- Let Event A be the event of getting a Head (H) on the coin.
- Let Event B be the event of getting a '3' on the die.

2. **Calculate the Probability of Event A (Coin)**:
- A fair coin has two sides: Head (H) and Tail (T).
- The probability of getting a Head (H) when tossing the coin is:
\[ P(A) = \frac{\text{Number of favorable outcomes for H}}{\text{Total outcomes for the coin}} = \frac{1}{2} \]

3. **Calculate the Probability of Event B (Die)**:
- A fair die has six faces numbered from 1 to 6.
- The probability of getting a '3' when rolling the die is:
\[ P(B) = \frac{\text{Number of favorable outcomes for 3}}{\text{Total outcomes for the die}} = \frac{1}{6} \]

4. **Combine the Probabilities**:
- Since the coin toss and die roll are independent events, the probability of both events happening (getting a Head and a '3') is the product of their individual probabilities:
\[ P(A \text{ and } B) = P(A) \times P(B) = \frac{1}{2} \times \frac{1}{6} \]

5. **Calculate the Final Probability**:
- Now, we multiply the two probabilities:
\[ P(A \text{ and } B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \]

### Final Answer:
The probability that a head appears on the coin and '3' appears on the die is \(\frac{1}{12}\).

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