Question

Two entities, X and Y, were identified as sole suspects for a cryptocurrency hack that pillaged $3 billion. Preliminary investigation determined a probability of 0.76 that X is guilty, and 0.24 probability that Y is responsible. After analyzing Tor traffic, investigators found that the perpetrator used a server, Spectre, which is accessible to 80 percent of Tor users. Suppose that Y was discovered possessing access to Spectre. There is no information regarding X's ability to access Spectre.

a). Given Y 's ability to access Spectre, what is the probability that Y carried out the hack? [Hint: Suppose that B = Y hacked, A = access to Spectre, You want P(B|A) = P(A|B) P(B)/(P(A|B)P(B) + P(A|~B)P(~B)) ]

b). Conditional on this information, what is the probability of X possessing access to Spectre? [Hint: Suppose that E = X has access to Spectre, and H = X hacked conditional on info from part (a) To be clear, P(H) = 1 - your answer for part (a) You want P(E) = P(E|H)P(H) + P(E|~H)P(~H) ]

Answer 1

Answer:-

Given That:-

Two entities, X and Y, were identified as sole suspects for a cryptocurrency hack that pillaged $3 billion. Preliminary investigation determined a probability of 0.76 that X is guilty, and 0.24 probability that Y is responsible. After analyzing Tor traffic, investigators found that the perpetrator used a server, Spectre, which is accessible to 80 percent of Tor users. Suppose that Y was discovered possessing access to Spectre. There is no information regarding X's ability to access Spectre.

P(Elliptic_Cracker being guilty) = 0.76

P(Bit_Basher being guilty) = 0.24

P(Using Spectre) = 0.80

a) Given that Bit_Basher accessed spectre

Thus P(Bit_Basher carried out the hack) =

b) Given the same information

Thus P(Elliptic_Cracker carried out the hack) =