A coin is tossed 1000 times with the following frequencies :
Head : 565, Tail : 435
Compute the probability for each event.

Answer

To solve the problem of computing the probability of getting heads and tails when a coin is tossed 1000 times, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Tosses**:
The total number of times the coin is tossed is given as 1000.

2. **Identify the Frequencies of Each Outcome**:
- Frequency of Heads (H) = 565
- Frequency of Tails (T) = 435

3. **Calculate the Probability of Getting Heads (P(H))**:
The formula for probability is:
\[ P(E) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]
For heads:
\[ P(H) = \frac{\text{Frequency of Heads}}{\text{Total Tosses}} = \frac{565}{1000} \]

4. **Simplify the Probability of Heads**:
To simplify \( \frac{565}{1000} \):
- Both 565 and 1000 can be divided by 5.
\[ \frac{565 \div 5}{1000 \div 5} = \frac{113}{200} \]
- In decimal form, \( \frac{113}{200} = 0.565 \).

5. **Calculate the Probability of Getting Tails (P(T))**:
For tails:
\[ P(T) = \frac{\text{Frequency of Tails}}{\text{Total Tosses}} = \frac{435}{1000} \]

6. **Simplify the Probability of Tails**:
To simplify \( \frac{435}{1000} \):
- Both 435 and 1000 can be divided by 5.
\[ \frac{435 \div 5}{1000 \div 5} = \frac{87}{200} \]
- In decimal form, \( \frac{87}{200} = 0.435 \).

7. **Final Results**:
- Probability of getting Heads (P(H)) = 0.565
- Probability of getting Tails (P(T)) = 0.435

### Summary of Probabilities:
- P(H) = 0.565
- P(T) = 0.435