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

Question

If the probability of a certain event is 55585558 55585558 , what is the probability of the event not happening?

Write all answers as simplified fractions.

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Solution

Break Down the Problem

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

Relevant Concepts

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

Analysis and Detail

  1. Given that the probability of the event happening P(A)=55585558100000000 P(A) = \frac{55585558}{100000000} :
    • First, we need to find the complement: P(A)=155585558100000000 P(A') = 1 - \frac{55585558}{100000000}
    • To perform the subtraction: P(A)=10000000055585558100000000=44414442100000000 P(A') = \frac{100000000 - 55585558}{100000000} = \frac{44414442}{100000000}

Verify and Summarize

  1. We should simplify the fraction 44414442100000000 \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: 44414442÷2100000000÷2=2220722150000000 \frac{44414442 \div 2}{100000000 \div 2} = \frac{22207221}{50000000}

Final Answer

The probability of the event not happening is 2220722150000000 \frac{22207221}{50000000}

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