Start from a prior probability and apply each likelihood ratio in likelihood_ratios as a piece of evidence. Return the final posterior probability.

Bayes is multiplication once you switch to odds:

• convert: $\text{odds} = p / (1-p)$
• multiply by every likelihood ratio in turn
• convert back: $p = \text{odds} / (1 + \text{odds})$

Input

prior = 0.01
likelihood_ratios = [10.0, 10.0]

Output

0.5025125628140703