Implementation of Bayes law(probabilities)

[dionys]

Hi guys
i know that i post a problem without my own answer but this problem is
very difficult for me and I'm very comfused.
The exercise says that we must implement the Bayes' Law to solve the exercise.My problem is that i can't distinguish and write down the events ):

Problem:In my kitchen i put my 10 forks in the left drawer and my 10 knifes in the right drawer.
before my room mate change something:
k=knife,f=forks
left drawer : (10f,0k)
right drawer: (0f,10k))

When my room-mate came he took 2 forks from the left drawer and he put them in the right drawer.

after my room mate's alteration:
left drawer : (8f,0k)
right drawer: (2f,10k)


After this action he chooses one piece(knife or fork) from the right drawer and he puts the piece in the left drawer.

left drawer : (9f,0k) or (8f,1k)
right drawer: (1f,10k) or (2f,9k)

After all these changes i come and choose one piece from 1 of the 2 drawers.
IF Is given that i hold a knife,what is the probability that i opened the left drawer?

 

[TenaliRaman]

apply simple Bayesian Law,
Let K be the event u pick the knife
Let L be the event u pick something from the left drawer
to find,
P(L/K)

simple Bayesian states,
P(L/K)*P(K) = P(K/L)*P(L)

can u find P(K),P(K/L),P(L) ??

-- AI

 

[wais]

In order to solve this problem using Bayes' Law, we need to define the events and their corresponding probabilities. In this case, the events we are interested in are:
- Event A: I hold a knife after all the changes have been made.
- Event B: I opened the left drawer.

Next, we need to determine the probabilities of each event. Since we are given that I hold a knife, the probability of event A is 1, or 100%. The probability of event B can be calculated by considering the total number of pieces in the left drawer (9) and the total number of pieces in both drawers (9+11=20). Therefore, the probability of event B is 9/20 or 0.45.

Using Bayes' Law, we can now calculate the probability of opening the left drawer given that I hold a knife:

P(B|A) = P(A|B) * P(B) / P(A)

P(B|A) = (1 * 0.45) / 1 = 0.45

Therefore, there is a 45% chance that I opened the left drawer if I am holding a knife.