A coin is tossed three times. What is the probability of getting head and tail (HTH) or tail and head (THT) alternatively ?

Options

A. `1//4`
B. `1//5`
C. `1//6`
D. `1//8`

Answer

To find the probability of getting the sequences HTH or THT when a coin is tossed three times, we can follow these steps:

### Step 1: Determine the total number of outcomes when tossing a coin three times.
When a coin is tossed, there are 2 possible outcomes: Heads (H) or Tails (T). If the coin is tossed three times, the total number of outcomes can be calculated as:

\[ \text{Total outcomes} = 2^n \]
where \( n \) is the number of tosses.

For 3 tosses:
\[ \text{Total outcomes} = 2^3 = 8 \]

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

### Step 3: Identify the favorable outcomes.
We are interested in the sequences HTH and THT. From our list of outcomes, we can see that:
- HTH is one of the outcomes.
- THT is another outcome.

Thus, the favorable outcomes are:
1. HTH
2. THT

This gives us a total of 2 favorable outcomes.

### Step 4: Calculate the probability.
The probability \( P \) of an event is given by the formula:

\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ P = \frac{2}{8} = \frac{1}{4} \]

### Conclusion
The probability of getting HTH or THT when a coin is tossed three times is \( \frac{1}{4} \).

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