three fair coins are tossed simultaneously . Find the propability of
getting atleast one head and one tail .

Options

A. `2/8`
B. `1/2`
C. `3/(10)`
D. `3/4`

Answer

To solve the problem of finding the probability of getting at least one head and one tail when tossing three fair coins, we can follow these steps:

### Step 1: Determine the Sample Space
When tossing three coins, each coin has two possible outcomes: heads (H) or tails (T). The total number of outcomes when tossing three coins can be calculated using the formula \(2^n\), where \(n\) is the number of coins.

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

The sample space (S) consists of the following outcomes:
1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT

### Step 2: Identify the Favorable Outcomes
Next, we need to identify the outcomes that satisfy the condition of having at least one head and one tail. The outcomes that meet this criterion are:
1. HHT
2. HTH
3. HTT
4. THH
5. THT
6. TTH

Counting these outcomes, we find that there are 6 favorable outcomes.

### Step 3: Calculate the Probability
The probability (P) of an event is given by the formula:

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

Substituting the values we found:

\[ P(E) = \frac{6}{8} = \frac{3}{4} \]

### Conclusion
Thus, the probability of getting at least one head and one tail when tossing three fair coins is:

\[ \frac{3}{4} \]