Probability of choosing marbles

1st attachment sets up the situation:
A bag contains marbles: 3 white (W), 5 black (B), 2 yellow (Y)
3 marbles are drawn (without replacement?)

Events:
A = WWY
B = BBX
C = "a special marble that is black" is drawn ...

... where X can stand for any color.

The second attachment has the questions:
(a) Find: (i) P(A) (ii) P(B) (iii) P(C) (iv) P(C|B)
(b) Are events B and C (i) mutually exclusive (ii) independent?
... then there are worked solutions.

None of the questions are numbered.
There are no letter (c) problems numbered 4 or 5 in the attachment.

Guessing that the circled solutions are the one you are interested in - these are for (a)ii and iv.
How would you go about finding the solution?

 

I hope you know that the solution uses Baye's theorem. The term 4C1 came from the fact that, while calculating P(B[itex]\cap[/itex]C) we calculate the probability when both B and C happen together. That means, you have two black marbles, a marble of another color and you have a special marble (let's call that dragonball) which in turn means that you have the dragonball, another black ball and a ball of another color. Now try and calculate the probability for this event : "Selecting 'the' dragonball, another black ball and a ball of another color". You should get the terms 4c1 and 5c1 now.

(NOTE: There is a far easier method of doing part IV than doing it by Baye's Theorem. Let me know if you want me to share that)

 

What is it about part iv that you don't understand?
Have you attempted it yourself yet? (Never mind the model answer.)
Do you know the formula for a conditional probability?

Adithyan has provided a major hint: "Bayes Theorem".
Do you know what that is?

 

That's OK.
(iv) requires you to learn about "conditional probability".
That is certainly in your course notes - but you may be expected to reason it out too.

afaict: P(C|B) is asking for the probability that you have drawn the special black marble given that the first two marbles drawn are black (but you don't know the third one's color).

This means you have one of: BBW, BBY, BBB - you don't know which it is.