With a $\mathrm{Beta}(\alpha,\beta)$ prior and observed successes and failures, return the probability that the next trial succeeds.

$$P(\text{next} = 1) = \frac{\text{successes} + \alpha}{\text{successes} + \text{failures} + \alpha + \beta}$$

Note this is the posterior mean, not the MAP. Predicting the next observation averages over the whole posterior rather than committing to its peak, which is why zero successes out of five does not predict zero.

Input

alpha = 1.0
beta = 1.0
successes = 0
failures = 5

Output

0.14285714285714285