If the probability of a certain event is 71807180, what are the odds against the event happening?

Break Down the Problem

1. Identify the probability of the event happening.
2. Calculate the probability of the event not happening.
3. Determine the odds against the event.

Relevant Concepts

1. The probability of an event happening is given as $P(E)$.
2. The probability of the event not happening is $P(\neg E) = 1 - P(E)$.
3. Odds against an event is calculated as $\text{Odds against} = \frac{P(\neg E)}{P(E)}$.

Analysis and Detail

1. Given that the probability of the event $P(E) = 71807180$:

   • Note that probability must be between 0 and 1. Thus, the given number seems to be improperly formatted. Assuming it's meant to be a fraction or a decimal probability, let's consider it a probability input mistake and rework it appropriately.

2. Without correct context or adjustment, let's state that probabilities should scale between 0 and 1. If interpreted differently,

   • Assuming $P(E) = \frac{718}{1000000} = 0.0000718$ (just an example of potential correction).

3. Now calculate $P(\neg E)$: $P(\neg E) = 1 - P(E) = 1 - 0.0000718 = 0.9999282$

4. Now calculate the odds against the event: $\text{Odds against} = \frac{P(\neg E)}{P(E)} = \frac{0.9999282}{0.0000718} \approx 13924.3$

Verify and Summarize

• The initial probability appears flawed under interpretation assumptions, but odds were calculated using approximated corrected probability values.
• The odds against the event happening, based on the calculated values, indicate strong unlikeliness.

Final Answer

The odds against the event happening are approximately $13924.3:1$.