If the probability of a certain event is 55585558 , what is the probability of the event not happening?Write all answers as simplified fractions.

Break Down the Problem

1. Identify the probability of the event occurring, denoted as $P(A)$.
2. Recall that the probability of the event not happening, denoted as $P(A')$, is calculated as $P(A') = 1 - P(A)$.

Relevant Concepts

3. The formula for the probability of the complement of an event is: $P(A') = 1 - P(A)$

Analysis and Detail

4. Given that the probability of the event happening $P(A) = \frac{55585558}{100000000}$:
   • First, we need to find the complement: $P(A') = 1 - \frac{55585558}{100000000}$
   • To perform the subtraction: $P(A') = \frac{100000000 - 55585558}{100000000} = \frac{44414442}{100000000}$

Verify and Summarize

5. We should simplify the fraction $\frac{44414442}{100000000}$.
   • The greatest common divisor (GCD) of 44414442 and 100000000 is 2.
   • Thus, we divide both the numerator and the denominator by 2: $\frac{44414442 \div 2}{100000000 \div 2} = \frac{22207221}{50000000}$

Final Answer

The probability of the event not happening is $\frac{22207221}{50000000}$