# negative binomial / wording issues

• Oct 29th 2012, 12:40 PM
negative binomial / wording issues
Q> 60% of the buses at my local bus stop are on route 39. If the routes of different buses are independent of each other, what is the probability that at least 4 buses that are not route 39 arrive before the 3rd route 39 bus ?

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I really don't understand these types of questions. The wording throws me for a loop :(

I know that it is probably neg binom but even with the formula I draw a blank for how to organize everything.

'at least' ? - is this the reason that this problem can't be done with only 1 application of the neg binom formula ?
'arrive before' ? - what if it were 'arrive on' or 'arrive after' ? how would these effect the total of successes+failures 'n' ?
• Oct 29th 2012, 08:16 PM
chiro
Re: negative binomial / wording issues

The best advice I can give for you is to think about what each distribution is modelling process wise and not mathematically/probabilistically/statistically.

For example binomial represents a physical model where you have n trials that are independent from each other with either a 0 or 1 outcome and then we sum up the outcomes to get X. Some say coin tosses or other things, but the idea is that you have n independent things with a success/fail for each and then look at the distribution for getting so many successes.

Now negative binomial processes model a process that waits for so many failures to occur. The geometric process is a special case waiting for one failure to occur but negative binomial allows arbitrary numbers of failures.

If you try and think in formulas only then I can see why this stuff would be confusing: the math needs to be supplemented by ideas with some kind of physical, or visual intuition and if your teacher hasn't communicated this then they aren't really a good teacher.
• Oct 30th 2012, 06:30 AM