If the probability of Sayna winning a badminton match is 0.81, what is the probability of her losing the match?

Answer

To find the probability of Sayna losing the badminton match given that the probability of her winning is 0.81, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Probability**:
The total probability of all possible outcomes in a situation must equal 1. In this case, the two possible outcomes are winning and losing the match.

\[ P(\text{Winning}) + P(\text{Losing}) = 1 \]

2. **Identify the Given Probability**:
We know that the probability of Sayna winning the match is given as:

\[ P(\text{Winning}) = 0.81 \]

3. **Set Up the Equation**:
Let \( P(\text{Losing}) \) be the probability of Sayna losing the match. According to the total probability rule, we can express this as:

\[ P(\text{Losing}) = 1 - P(\text{Winning}) \]

4. **Substitute the Known Value**:
Now, substitute the value of \( P(\text{Winning}) \) into the equation:

\[ P(\text{Losing}) = 1 - 0.81 \]

5. **Calculate the Probability of Losing**:
Perform the subtraction:

\[ P(\text{Losing}) = 1 - 0.81 = 0.19 \]

6. **Conclusion**:
Therefore, the probability of Sayna losing the badminton match is:

\[ P(\text{Losing}) = 0.19 \]

### Final Answer:
The probability of Sayna losing the match is **0.19**.

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