Answer:
The probabilities of each suspect being guilty are
[tex]P(S) = 0.243[/tex]
[tex]P(W) = 0.027[/tex]
[tex]P(T) = 0.001[/tex]
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
[tex]P(S) = ^N C_k * p^k * q^{N - k }[/tex]
Here C stands for combination
[tex]P(S) = ^3 C_2 * (0.90)^2 * (0.10)^{3 - 2 }[/tex]
[tex]P(S) = 0.243[/tex]
Generally the probability the woman being guilty is mathematically represented as
[tex]P(W) = ^N C_u * p^u * q^{N - u }[/tex]
=> [tex]P(W) = ^3 C_1 * p^1 * q^{3 - 1 }[/tex]
=> [tex]P(W) = 0.027[/tex]
Generally the probability the tall man being guilty is mathematically represented as
[tex]P(T) = ^N C_h * p^h * q^{N - h }[/tex]
=> [tex]P(T) = ^3 C_0 * p^0 * q^{3 - 0 }[/tex]
=> [tex]P(T) = 0.001[/tex]
