Three coins are tossed simultaneously. What is the probability that head and tail show alternately. (i.e., HTH or THT )?

Options

A. `(3)/(8)`
B. `(1)/(4)`
C. `(1)/(8)`
D. `(1)/(2)`

Answer

To find the probability that heads and tails show alternately when three coins are tossed, we can follow these steps:

### Step 1: Determine the total number of outcomes when tossing three coins.
When we toss a coin, there are 2 possible outcomes: heads (H) or tails (T). Therefore, when tossing three coins, the total number of outcomes can be calculated as:
\[ \text{Total outcomes} = 2^3 = 8 \]
The possible outcomes are:
1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT