Is the problem allowing you to choose "k", or does it want the maximum or minimum value? Because it is asking two questions: the probability and the value of k.
I've been going in circles trying to work out the solution to this problem:
Suppose that 10 cards, of which 7 are red and 3 are green, are put at random into 10 envelopes, of which 7 are red and 3 are green, so that each envelope contains one card. Determine the probability that exactly k envelopes will contains a card with a matching colour (k= 1,2,......,10)
By intuition I realise k cannot be less than 4 but then I get confused.
Any help would be appreciated!
Is the problem allowing you to choose "k", or does it want the maximum or minimum value? Because it is asking two questions: the probability and the value of k.
The questions gives us that the value of k goes from 0 through to 10... I interpreted the question to be asking for the probabilities of each if these events ie prob of 10 matching pairs, 9 matching pairs etc.
I'm having trouble determining these probabilities, I'm not sure how to count the outcomes for the respective events and without that I can't determine the probabilities, can I?
The only thing I know Is that there cannot be less than 4 matching pairs because even if all three green cards go into red envelopes and then three red cards go into green envelopes 4 pairs of red cards and red envelopes remain...