Boy, wonder who’s who.
So, theoretically, if one is at 95%, do you mean that the second is at a 65-70% or that the odds of getting both at 65-70%? Because of it it’s the latter….
To solve for the odds of the second event (let's call it Event Gabe), we can use the formula for the probability of two independent events happening together. The probability of both events X and Gabe occurring (P(C ∩ Gabe)) is related to the probabilities of X and Gabe as follows:
\[
P(X \cap Gabe) = P( ) \times P(Gabe \mid X)
\]
where:
- \( P(X) \) is the probability of Event X (95% or 0.95),
- \( P(Gabe \mid X) \) is the probability of Event Gabe happening given that Event X has occurred.
You are given that the probability of both events happening together is between 65% and 70% (or 0.65 to 0.70). So, we have the equation:
\[
P(X \cap Gabe) = P(C) \times P(Gabe) = 0.65 \text{ to } 0.70
\]
Now, solve for \( P(Gabe) \):
\[
P(Gabe) = \frac{P(X \cap Gabe)}{P(X)}
\]
Substitute the values:
\[
P(Gabe) = \frac{0.65}{0.95} \approx 0.684 \quad \text{to} \quad P(Gabe) = \frac{0.70}{0.95} \approx 0.737
\]
So, the probability of Event Gabe occurring is approximately between **68.4% and 73.7%**.