A coin is tossed three times. The probability of getting head and tail alternately, is

Options

A. `1//8`
B. `1//2`
C. `1//4`
D. none of these

Answer

To find the probability of getting heads and tails alternately when a coin is tossed three times, we can follow these steps:

### Step 1: Determine the Total Outcomes
When a coin is tossed three times, each toss has 2 possible outcomes: Heads (H) or Tails (T). Therefore, the total number of outcomes when tossing the coin three times is calculated as follows:

\[ \text{Total Outcomes} = 2^3 = 8 \]

### Step 2: List All Possible Outcomes
The possible outcomes when tossing the coin three times are:
1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT

### Step 3: Identify Favorable Outcomes
Next, we need to identify the outcomes that represent heads and tails alternating. For three tosses, the sequences that meet this criterion are:
1. HTH
2. THT

Thus, there are 2 favorable outcomes.

### Step 4: Calculate the Probability
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of getting heads and tails alternately is:

\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{8} = \frac{1}{4} \]

### Final Answer
The probability of getting heads and tails alternately when a coin is tossed three times is \(\frac{1}{4}\).

---