Witness says the cab was blue

In a town $85\%$ of cabs are green and the remaining $15\%$ are blue. After a hit-and-run, a witness reports that the cab was blue. Tests show the witness identifies cab colour correctly $80\%$ of the time. Given the report, how likely is it that the cab really was blue?

$12/29\approx41\%$. By Bayes, $P(\text{blue}\mid\text{says blue})=\dfrac{0.15\times0.8}{0.15\times0.8+0.85\times0.2}=\dfrac{0.12}{0.29}$. The low base rate of blue cabs outweighs the witness's reliability.