TITLE: Drawing from bucket: likelihood of consecutive draws.
QUESTION [0 upvotes]: Drawing from a bucket of: 3 red balls and 10 green balls, what is the likelihood of the 3 red balls being drawn consecutively? What is the likelihood of all 3 being drawn in some sequence of 4 draws? 5 draws? .... taking all 13 draws to see all 3?
How would I create a distribution of the likelihoods from 3 (all consecutive) to 13 (as separately drawn as possible)?

REPLY [0 votes]: You have ${13 \choose 3}$ orders for drawing all $13$ balls.  A run of three can start at $11$ positions, so the chance of getting the three consecutive is $\frac {11}{13 \choose 3}$  Count the number of orders that get you three within a span of four (but presumably not including the ones that have three in a row) and you will get that one.
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