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The probability of happening of an event...

The probability of happening of an event is `3/5`. Find the probability of not happening the event.

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To find the probability of not happening of an event when the probability of the event happening is given, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Probability of the Event**: The probability of the event happening, denoted as P(A), is given as \( P(A) = \frac{3}{5} \). 2. **Use the Complement Rule**: The probability of the event not happening, denoted as P(A'), can be found using the complement rule. The sum of the probabilities of an event happening and not happening is always equal to 1. This can be expressed as: \[ P(A) + P(A') = 1 \] 3. **Substitute the Known Probability**: We already know \( P(A) = \frac{3}{5} \). We can substitute this value into the equation: \[ \frac{3}{5} + P(A') = 1 \] 4. **Solve for P(A')**: To find \( P(A') \), we can rearrange the equation: \[ P(A') = 1 - \frac{3}{5} \] To perform the subtraction, convert 1 into a fraction with a common denominator: \[ P(A') = \frac{5}{5} - \frac{3}{5} = \frac{2}{5} \] 5. **Conclusion**: Therefore, the probability of the event not happening is: \[ P(A') = \frac{2}{5} \] ### Final Answer: The probability of not happening the event is \( \frac{2}{5} \). ---

To find the probability of not happening of an event when the probability of the event happening is given, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Probability of the Event**: The probability of the event happening, denoted as P(A), is given as \( P(A) = \frac{3}{5} \). 2. **Use the Complement Rule**: ...
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