Combinatorics/probability problem

[l0ner]

Hello everyone! I have a question I have not been able to solve.

There are three boxes.



Box 1 - three red, three white balls,

Box 2 - two red and three white balls

Box 3 - 4 red and 2 white balls.



A ball is picked at random from a randomly picked box, where the probabilities of choosing each box is 1:2:1.



a) What is the probability that a red ball is picked



b) Determine the ratio between the probability that a white ball is picked and the probability that a red ball is picked



c) If a red ball is picked, determine the probability that it was chosen from the second box.

 

[Dr.Peterson]

Please show us whatever work you have done (or at least one attempt), so we can see what methods you are trying and whether you are doing it correctly.

It will also be helpful if you tell us where you are in your learning of probability. Is this your first exposure to the subject? Is this problem for a class in which you have just learned some techniques that would likely be useful here? What approach(es) are you comfortable with (e.g. tree diagrams, multiplying probabilities, combinations, permutations, distributions, conditional probability, ... ?

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[pka]

There are three boxes.
Box 1 - three red, three white balls,
Box 2 - two red and three white balls
Box 3 - 4 red and 2 white balls.
A ball is picked at random from a randomly picked box, where the probabilities of choosing each box is 1:2:1.
a) What is the probability that a red ball is picked

Here is a start.
The probability that a red ball is chosen from box I is:
\(\mathcal{P}(R\cap B_1)=\)
\(\mathcal{P}(R | B_1)(\mathcal{P}( B_1)=\)
\(\left(\dfrac{3}{6}\right) \left(\dfrac{1}{4}\right)=~?\) Why?
Please answer and post your own work.