An unbiased coin is tossed 20 times. In this experiment , 11 heads and 9 tails were received. Calculate the probability of receiving head and the probability of receiving tail on the basis of the experiment .

Answer

To solve the problem of calculating the probability of receiving heads and tails based on the experiment of tossing an unbiased coin 20 times, we can 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 20.

2. **Count the Number of Heads and Tails**:
- From the experiment, we have:
- Number of Heads (H) = 11
- Number of Tails (T) = 9

3. **Calculate the Probability of Heads**:
- The probability of an event is calculated using the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- For heads:
\[ P(\text{Heads}) = \frac{\text{Number of Heads}}{\text{Total Tosses}} = \frac{11}{20} \]
- To convert this into decimal form:
\[ P(\text{Heads}) = 0.55 \]

4. **Calculate the Probability of Tails**:
- Similarly, for tails:
\[ P(\text{Tails}) = \frac{\text{Number of Tails}}{\text{Total Tosses}} = \frac{9}{20} \]
- Converting this into decimal form:
\[ P(\text{Tails}) = 0.45 \]

5. **Final Results**:
- The probability of receiving heads is \( P(\text{Heads}) = 0.55 \).
- The probability of receiving tails is \( P(\text{Tails}) = 0.45 \).

### Summary of Results:
- Probability of Heads: \( P(\text{Heads}) = 0.55 \)
- Probability of Tails: \( P(\text{Tails}) = 0.45 \)