4. There are three equally likely suspects for a crime. Suspect A is a short man, Suspect B is a tall man, and Suspect C is a tall woman. Only one of them was at the crime scene. Two witnesses report seeing a short person at the crime scene, and one witness reports seeing a woman at the crime scene. In your experience, witness reports are 90% reliable (each witness, independently, is 90% likely to make a correct report, and 10% likely to make a false report). Based only on the testimony of these three witnesses, what are the probabilities of each suspect being guilty

The probabilities of each suspect being guilty are

Step-by-step explanation:

Generally from the question we are told that

The number of suspects is N = 3

The number of witnesses that reported seeing a short man is k = 2

The number of witnesses that reported seeing a woman is u = 1

The probability of a witness being correct is p = 0.90

The probability of a witness not being correct is q 0.10

Generally the number of  witnesses that reported seeing a tall  man is h =  0

Generally the probability the short man being guilty is mathematically represented as

Here C stands for combination

Generally the probability the woman being guilty is mathematically represented as

=>      

=>      

Generally the probability the  tall man being guilty is mathematically represented as

=>      

=>      

b