three fair coins are tossed simultaneously . Find the propability of
getting atlest two heads .

Options

A. `3/8`
B. `7/8`
C. `1/2`
D. `1/4`

Answer

To find the probability of getting at least two heads when three fair coins are tossed, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Sample Space**:
When three coins are tossed, each coin has 2 possible outcomes: Heads (H) or Tails (T). Therefore, the total number of outcomes when three coins are tossed can be calculated as:
\[ \text{Total Outcomes} = 2^3 = 8 \]
The sample space (S) is:
\[ S = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \} \]

2. **Identify the Favorable Outcomes**:
We need to find the outcomes that have at least 2 heads. The favorable outcomes are:
- HHH (3 heads)
- HHT (2 heads)
- HTH (2 heads)
- THH (2 heads)

Thus, the favorable outcomes (E) are:
\[ E = \{ HHH, HHT, HTH, THH \} \]

3. **Count the Number of Favorable Outcomes**:
The number of favorable outcomes is:
\[ |E| = 4 \]

4. **Calculate the Probability**:
The probability (P) of getting at least 2 heads is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ P(E) = \frac{|E|}{|S|} = \frac{4}{8} = \frac{1}{2} \]

### Final Answer:
The probability of getting at least two heads when three fair coins are tossed is:
\[ \frac{1}{2} \]