Three coins are tossed .Find the probability of heads .

Options

A. `(1)/(6)`
B. `(1)/(8)`
C. `(1)/(4)`
D. `(1)/(3)`

Answer

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

### Step 1: Determine the total number of outcomes
When three coins are tossed, each coin has two possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes when tossing three coins can be calculated as:
\[ \text{Total Outcomes} = 2^n \]
where \( n \) is the number of coins. In this case, \( n = 3 \):
\[ \text{Total Outcomes} = 2^3 = 8 \]

### Step 2: List all possible outcomes
The possible outcomes when tossing three coins are:
1. TTT (Tail, Tail, Tail)
2. TTH (Tail, Tail, Head)
3. THT (Tail, Head, Tail)
4. THH (Tail, Head, Head)
5. HTT (Head, Tail, Tail)
6. HTH (Head, Tail, Head)
7. HHT (Head, Head, Tail)
8. HHH (Head, Head, Head)

### Step 3: Count the favorable outcomes for getting heads
We are interested in the scenario where all three coins show heads (HHH). There is only one favorable outcome:
- HHH

### Step 4: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
In this case, the number of favorable outcomes (getting heads in all three coins) is 1, and the total number of outcomes is 8. Therefore, the probability is:
\[ \text{Probability} = \frac{1}{8} \]

### Final Answer
The probability of getting heads when three coins are tossed is:
\[ \frac{1}{8} \]

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