Three unbiased coins are tossed. Find the probability of getting atleast two heads.

Options

A. `2/3`
B. `2/5`
C. `1/4`
D. `1/2`

Answer

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

### Step 1: Determine the Sample Space
When three coins are tossed, each coin can either show heads (H) or tails (T). The total number of outcomes when tossing three coins can be calculated as follows:
- Each coin has 2 outcomes (H or T).
- Therefore, for 3 coins, the total number of outcomes = \(2^3 = 8\).

The sample space (all possible outcomes) is:
1. HHH
2. HHT
3. HTH
4. THH
5. HTT
6. THT
7. TTH
8. TTT

### Step 2: Identify Favorable Outcomes
Next, we need to find the outcomes that have at least two heads. The favorable outcomes are:
1. HHH (3 heads)
2. HHT (2 heads)
3. HTH (2 heads)
4. THH (2 heads)

Counting these, we find there are 4 favorable outcomes.

### Step 3: Calculate the Probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]

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

### Conclusion
Thus, the probability of getting at least two heads when tossing three unbiased coins is \(\frac{1}{2}\).

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