three fair coins are tossed simultaneously . Find the propability of
getting more heads than the number of tails.

Options

A. 2
B. `7//8`
C. `5/8`
D. `1/2`

Answer

To find the probability of getting more heads than tails when tossing three fair coins, we can follow these steps:

### Step 1: Determine the Sample Space
When tossing 3 coins, each coin has 2 possible outcomes: heads (H) or tails (T). The total number of outcomes can be calculated using the formula \(2^n\), where \(n\) is the number of coins.

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

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 where the number of heads is greater than the number of tails. With 3 coins, this can happen in the following scenarios:
- 3 heads and 0 tails (HHH)
- 2 heads and 1 tail (HHT, HTH, THH)

The favorable outcomes are:
1. HHH (3 heads, 0 tails)
2. HHT (2 heads, 1 tail)
3. HTH (2 heads, 1 tail)
4. THH (2 heads, 1 tail)

So, the total number of favorable outcomes is 4.

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

\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]

Substituting the values we found:

\[ \text{Probability} = \frac{4}{8} = \frac{1}{2} \]

### Final Answer
Thus, the probability of getting more heads than tails when tossing three fair coins is:

\[ \frac{1}{2} \]

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