A coin is tossed 40 times and head appears 25 times. What is the probability of getting a tail.

Answer

To solve the problem of finding the probability of getting a tail when a coin is tossed 40 times and heads appear 25 times, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Trials**:
The total number of times the coin is tossed is given as 40.
\[ \text{Total Trials} = 40 \]

2. **Determine the Number of Heads**:
The problem states that heads appear 25 times.
\[ \text{Number of Heads} = 25 \]

3. **Calculate the Number of Tails**:
Since the coin can either show heads or tails, we can find the number of tails by subtracting the number of heads from the total trials.
\[ \text{Number of Tails} = \text{Total Trials} - \text{Number of Heads} = 40 - 25 = 15 \]

4. **Define the Probability Formula**:
The probability of an event is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]

5. **Substitute the Values into the Probability Formula**:
Here, the number of favorable outcomes is the number of tails (15), and the total outcomes are the total trials (40).
\[ \text{Probability of Tails} = \frac{\text{Number of Tails}}{\text{Total Trials}} = \frac{15}{40} \]

6. **Simplify the Fraction**:
To simplify \(\frac{15}{40}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 5.
\[ \frac{15 \div 5}{40 \div 5} = \frac{3}{8} \]

7. **Final Answer**:
Therefore, the probability of getting a tail when the coin is tossed 40 times is:
\[ \text{Probability of Tails} = \frac{3}{8} \]