If the odds against an event happening are 70577057 , what is the probability of the event happening?

1. ### Break Down the Problem

We are given the odds against an event happening, which is 70,577,057. To find the probability of the event occurring, we will first need to understand the relationship between odds and probability.

2. ### Relevant Concepts

The odds against an event occurring can be expressed as: $\text{Odds against} = \frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}$ From this, we can derive the probability $P$ of the event occurring using the formula: $P(\text{event}) = \frac{1}{\text{Odds against} + 1}$

3. ### Analysis and Detail

1. Determine the number of unfavorable outcomes: This is given as 70,577,057.
2. Determine the number of favorable outcomes: This is 1, because there is one event that is happening.
3. Calculate the total: $\text{Total Outcomes} = 70,577,057 + 1 = 70,577,058$
4. Calculate the probability: $P(\text{event}) = \frac{1}{70,577,058}$

4. ### Verify and Summarize

The calculation steps have been verified:

• Adding unfavorable and favorable outcomes gives a total of $70,577,058$.
• The probability calculated is $\frac{1}{70,577,058}$.

Final Answer

$P(\text{event}) = \frac{1}{70,577,058} \approx 0.0000000142$