Three coins are tossed .Find the probability of exactly 2 heads .

Options

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

Answer

To find the probability of getting exactly 2 heads when tossing three coins, we can follow these steps:

### Step 1: Determine the total outcomes
When tossing three coins, each coin has 2 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. Here, \( n = 3 \):
\[ \text{Total Outcomes} = 2^3 = 8 \]

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

### Step 3: Identify favorable outcomes for exactly 2 heads
Next, we need to find the outcomes that have exactly 2 heads. The favorable outcomes are:
1. HHT
2. HTH
3. THH

Thus, there are 3 favorable outcomes.

### Step 4: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{3}{8} \]

### Final Answer
The probability of getting exactly 2 heads when tossing three coins is:
\[ \frac{3}{8} \]

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