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, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between winning and losing probabilities**:
The probability of an event occurring plus the probability of that event not occurring equals 1. In this case, the event is Sayna winning the match, and the event not occurring is her 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**:
Using the relationship established in step 1, we can substitute the known probability into the equation:

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

4. **Solve for the probability of losing**:
To find the probability of losing, we can rearrange the equation:

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

Substituting the value of \( P(\text{Winning}) \):

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

5. **Calculate the result**:
Performing the subtraction:

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

Thus, the probability of Sayna losing the badminton match is **0.19**.