Bayes Posterior

Compute the posterior probability of hypothesis $H_{1}H\_1$ from its prior probability and the likelihood of the observed evidence under $H_{1}H\_1$ and under $H_{0}H\_0$.

Implement solve(prior, likelihood_h1, likelihood_h0).

Returns. Return a float in $[0,1][0,\; 1]$. The prior of $H_{0}H\_0$ is $1-\text{prior}1-\backslash text\{prior\}$. The prior and both likelihoods must lie in $[0,1][0,\; 1]$, and if the total evidence $P(e)P(e)$ is zero the posterior does not exist; both cases raise ValueError.

Examples

Example 1

Input:

solve(0.5, 0.8, 0.2)

Output:

0.8

Example 2

Input:

solve(0.01, 0.9, 0.05)

Output:

0.153846