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It is given that the probability of winn...

It is given that the probability of winning a game is `(3)/(7)`. What is the probability of lossing the game.

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To find the probability of losing the game when the probability of winning is given, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Total Probability**: The total probability of all possible outcomes (winning and losing) in a game is always equal to 1. \[ P(\text{Winning}) + P(\text{Losing}) = 1 \] 2. **Identify the Given Probability**: We are given that the probability of winning the game is \[ P(\text{Winning}) = \frac{3}{7} \] 3. **Set Up the Equation**: Substitute the given probability into the total probability equation: \[ \frac{3}{7} + P(\text{Losing}) = 1 \] 4. **Isolate the Probability of Losing**: To find the probability of losing, we can rearrange the equation: \[ P(\text{Losing}) = 1 - \frac{3}{7} \] 5. **Convert 1 to a Fraction**: To perform the subtraction, we can express 1 as a fraction with a denominator of 7: \[ 1 = \frac{7}{7} \] 6. **Perform the Subtraction**: Now we can subtract the fractions: \[ P(\text{Losing}) = \frac{7}{7} - \frac{3}{7} = \frac{7 - 3}{7} = \frac{4}{7} \] 7. **Conclusion**: Therefore, the probability of losing the game is \[ P(\text{Losing}) = \frac{4}{7} \] ### Final Answer: The probability of losing the game is \(\frac{4}{7}\).
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