A experiment consists of flipping a coin and then flipping it a second time if head occurs. If a tail occurs on the first flip, then a six-faced die is tossed once. Assuming that the outcomes are equally likely. What is the probability of getting one head and one tail?

Options

A. A. `(1)/(4)`
B. B. `(1)/(36)`
C. C. `(1)/(6)`
D. D. `(1)/(8)`

Answer

To solve the problem step by step, let's break down the experiment and find the required probability.

### Step 1: Understand the Experiment
The experiment consists of:
1. Flipping a coin.
2. If the first flip is Heads (H), flip the coin again.
3. If the first flip is Tails (T), roll a six-faced die.

### Step 2: Determine Possible Outcomes
1. **If the first flip is Heads (H)**:
- The second flip can also be Heads (H) or Tails (T).
- Possible outcomes:
- HH (Head on first flip, Head on second flip)
- HT (Head on first flip, Tail on second flip)

2. **If the first flip is Tails (T)**:
- The die can show any of the numbers from 1 to 6.
- Possible outcomes:
- T1, T2, T3, T4, T5, T6 (Tails on first flip, and die shows 1 to 6)

### Step 3: List All Possible Outcomes
Combining both scenarios, the total sample space of outcomes is:
- HH
- HT
- T1
- T2
- T3
- T4
- T5
- T6

This gives us a total of 8 possible outcomes.

### Step 4: Identify Favorable Outcomes
We need to find the probability of getting one Head and one Tail. The only outcome that satisfies this condition is:
- HT (Head on first flip, Tail on second flip)

Thus, there is only **1 favorable outcome** (HT).

### Step 5: Calculate the Probability
The probability \( P \) of an event is given by:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
Substituting the values:
\[ P = \frac{1}{8} \]

### Final Answer
The probability of getting one Head and one Tail is \( \frac{1}{8} \).

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