Posterior probability of being believed LOW

Posterior probability of being believed HIGH

Product Quality LOW

(proportion $\pi$ )

$\delta +\frac{{\left(1-\delta \right)}^2\pi }{1-\delta \pi }$

$\frac{\left(1-\delta \right)\left(1-\pi \right)}{1-\delta \pi }$

Product Quality HIGH

(proportion $1-\pi$ )

$\frac{\left(1-\delta \right)\pi }{1-\delta \pi }$

$\frac{1-\pi }{1-\delta \pi }$