In a badminton match between Rajesh and Joseph, the probability of winning of Rajesh is 0.58. Find the probability of :
(i) not winning of Rajesh,

Answer

To find the probability of Rajesh not winning the badminton match, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Probability of Winning**:
The probability of Rajesh winning the match is given as \( P(\text{Rajesh wins}) = 0.58 \).

2. **Understand Total Probability**:
The total probability of all possible outcomes in a probability scenario is always equal to 1. In this case, the two possible outcomes are Rajesh winning or Rajesh not winning.

3. **Set Up the Equation**:
Since there are only two outcomes (Rajesh wins or Rajesh does not win), we can express the probability of Rajesh not winning as:
\[ P(\text{Rajesh does not win}) = 1 - P(\text{Rajesh wins}) \]

4. **Substitute the Known Value**:
Now, substitute the known probability of Rajesh winning into the equation:
\[ P(\text{Rajesh does not win}) = 1 - 0.58 \]

5. **Perform the Calculation**:
Calculate the result:
\[ P(\text{Rajesh does not win}) = 1 - 0.58 = 0.42 \]

6. **Conclusion**:
Therefore, the probability of Rajesh not winning the match is \( 0.42 \).

### Final Answer:
The probability of Rajesh not winning is \( 0.42 \).

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