This question is solved one - but I am trying to find flaw in my understanding of the situation. The question is as follows:
The blue M&M was introduced in 1995. Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan). Afterward it was (24% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown).
A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996. He won't tell me which is which, but he gives me one M&M from each bag. One is yellow and one is green. What is the probability that the yellow M&M came from the 1994 bag?
I am trying to find the sample space first, and it seems there is flaw in my understanding of the problem. Need help in understanding that flaw and if possible please let me know how you would solve it (with or without Bayes' Theorem). I am a beginner (not a student though) and want to understand different aspects from which this problem can be viewed. 2-3 approaches should suffice. I know that this will call extra pain - I want to thank you in advance.
Let B1 (1994) and B2 (1996) are two bags. The sample space should comprise of following events -
- B1 x B2 = 36 events - That is an ordered pair containing first M&M from B1 and the other from B2.
- B2 x Tan (from B1) = 6 events
- B1 x Blue (from B2) = 6 events
So in total we have 48 possible events. (Please confirm)
However since the weight of each event varies because of difference in frequency of each colour the probability of each of these 48 events is not equally likely. Sum of the probability of all these events should be unity though.
P(Y/B1) . P(G/B2) = .04
What should I do from here on ?