There is a murder case with two suspects, Jane and Jack. The murder took place in the kitchen and the victim was stabbed with a knife.

There is a murder case with two suspects, Jane and Jack.
The murder took place in the kitchen and the victim was stabbed with a knife.
Jane was supposedly spotted by a witness outside in the garden at the time of the murder. As she is skilled at throwing knives, the probability of her being the murderer if she was outside is 0.1 and the probability of her being the murderer if the witness was wrong is 0.95. The overall calculated probability of her being the murderer is 0.2/0.7
Jack the second suspect was seen washing his hands a bit after the murder happened. As he’s a hygiene freak though, that’s not entirely unusual. The probability that Jack washed his hands given he isn’t the murderer is 0.25 and the probability that he washed his hands given that he is the murderer is 0.95. What’s the probability that he’s the murderer.
So basically for Jack:
P(W|M’)=0.25
P(W|M)=0.95
What is P(M)?
What is the probability that they are both guilty of the murder? And are these independent events?
 
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