A New York City cab was involved in a hit-and-run accident last night. Five witnesses reported the incident, four of whom said that the cab was green and one of whom said that the cab was yellow. Assume each witness correctly identifies the colour of a cab with probability 2/3. It is known that 85% of registered cabs in New York City are yellow and 15% are green. Based on this information, what is the probability that the cab was green?
Answer choices:
- 41.5%
- 15.0%
- 58.5%
- 88.9%
My Progress
I don't know what the prior probability is and have particular difficulty calculating the likelihood.
I attempted to use binomial expansion to calculate the likelihood this way:
$$\frac{5!}{4!(5-4)!} \times 0.15^4 \times 0.85^1$$
- But when I calculate the likelihood and subsequently the posterior probability, it does not match any of the above choices.