Determine the probability of event $$ E $$ if the odds against $$ E $$ are 26 to 25 . Note:For any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places.

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Let the probability of event $$ E $$ be $$ p $$.

The odds against $$ E $$ are given as 26 to 25, which means:
$$
\frac{\text{Probability of not }E}{\text{Probability of }E} = \frac{26}{25}.
$$

Since the probability of not $$ E $$ is $$ 1 - p $$, we have:
$$
\frac{1-p}{p} = \frac{26}{25}.
$$

Solving for $$ p $$:

1. Cross multiply:
   $$
   25(1-p) = 26p.
   $$

2. Expand the left-hand side:
   $$
   25 - 25p = 26p.
   $$

3. Combine like terms:
   $$
   25 = 26p + 25p = 51p.
   $$

4. Solve for $$ p $$:
   $$
   p = \frac{25}{51}.
   $$

Thus, the probability of event $$ E $$ is:
$$
\boxed{\frac{25}{51}}.
$$
The probability of event $$ E $$ is $$ \frac{25}{51} $$.

Determine the probability of event if the odds against are 26 to 25 .
Note:For any final answer that has up to four decimal places, enter your answer without rounding
the number. For any answers with more than four decimal values, round your final answer to four
decimal places.

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Determine the probability of event if the odds against are 26 to 25 . Note:For any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places.