When a coin was tossed 200 times, we obtained Head : 118 times and Tail: 82 times. When the coin is tossed at random, what is the probability of getting
(i) ahead?
(ii) a tail?

Answer

To solve the problem, we need to calculate the probability of getting heads and tails when a coin is tossed based on the given data.

### Step-by-Step Solution:

1. **Understand the Data**:
- The coin was tossed 200 times.
- Heads were obtained 118 times.
- Tails were obtained 82 times.

2. **Calculate the Probability of Getting Heads**:
- The formula for probability is given by:
\[ P(\text{Heads}) = \frac{\text{Number of Heads}}{\text{Total Tosses}} \]
- Substitute the values:
\[ P(\text{Heads}) = \frac{118}{200} \]

3. **Simplify the Probability of Getting Heads**:
- To simplify \(\frac{118}{200}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD).
- The GCD of 118 and 200 is 2.
- Therefore:
\[ P(\text{Heads}) = \frac{118 \div 2}{200 \div 2} = \frac{59}{100} \]

4. **Calculate the Probability of Getting Tails**:
- Similarly, we use the formula for probability:
\[ P(\text{Tails}) = \frac{\text{Number of Tails}}{\text{Total Tosses}} \]
- Substitute the values:
\[ P(\text{Tails}) = \frac{82}{200} \]

5. **Simplify the Probability of Getting Tails**:
- To simplify \(\frac{82}{200}\), we can divide both the numerator and the denominator by their GCD.
- The GCD of 82 and 200 is 2.
- Therefore:
\[ P(\text{Tails}) = \frac{82 \div 2}{200 \div 2} = \frac{41}{100} \]

### Final Answers:
- (i) The probability of getting a head is \(\frac{59}{100}\).
- (ii) The probability of getting a tail is \(\frac{41}{100}\).