Probability question - Bayes Theorem

1. A judge is 0.35 sure that a robber is guity. Witness A will lie with a probability of 0.25 when the robber is guilty and would only tells the truth if robber is innocent. Witness B will lie with probability 0.30 if robber is innocent and would only tell the truth if the robber is guilty.

What is the probability that the robber is guity given that both witnesses gave testimony that are conflicting

2. In addition to the previous question, another witness inform the judge that the probability of the robber being left handed is 0.85. If 0.23 of the population is left-handed and so does the robber, with all these additional information, how certain can the judge be of the guilt of the robber?

For the 1st part of the question do I use Baye's Theorem?
e.g. Required probability = 0.25*0.35/[(0.25*0.35)+(0.30*0.65)]= 0.30 - using Baye's Theorem

And can anyone help me with the 2nd part. I have no idea on how to use the information to answer the question. Thanks !

tvtokyo said:

1. A judge is 0.35 sure that a robber is guity. Witness A will lie with a probability of 0.25 when the robber is guilty and would only tells the truth if robber is innocent. Witness B will lie with probability 0.30 if robber is innocent and would only tell the truth if the robber is guilty.

Click to expand...

You say that witness A will only tell the truth if the robber is innocent. That would mean that if the robber is guilty than witness A will always lie, not only 25% of the time but all the time (100%). Do you mean to say always instead of only?? Same with witness B.

Yes. I meant that. Do you know how to approach the 2nd part? Thanks

tvtokyo said:

1. A judge is 0.35 sure that a robber is guity. Witness A will lie with a probability of 0.25 when the robber is guilty and would only tells the truth if robber is innocent. Witness B will lie with probability 0.30 if robber is innocent and would only tell the truth if the robber is guilty.
...

Click to expand...

Restricting ourselves to the first problem, it doesn't seem as though we have enought information to solve the problem. This was alluded to in the other post, however it is also possible for the statements of witness A as to the guilt or innocence of the 'robber' to be independent. For example, for Witness A
If guilty: Innocent 25% of the time, Guilty 75% of the time
If Innocent: Innocent 90% of the time, Guilty 10% of the time.
Just what are the values for Innocent?

BTW: Does the use of the word robber to describe the person mean the person has already been found guilty or just that the person has robbed before?

You can treat the robber as a normal person i.e. not guilty yet