Edward C. answered • 02/10/15

Caltech Grad for math tutoring: Algebra through Calculus

You need to make a list of all the possible sequences of outcomes and then discard the ones that do not satisfy your criteria. But don't worry, since there is a maximum of 4 calls there are only 2^4 = 16 possible outcomes, which are

SSSS SSSN SSNS SSNN

SNSS SNSN SNNS SNNN

NSSS NSSN NSNS NSNN

NNSS NNSN NNNS NNNN

Calls continue until two successive sales are made, so the entire first row collapses to just a single SS. And the first two elements of the third row collapse to NSS.

Calls also stop if two calls result in no sale, so the last two elements of the second row collapse to SNN, the last two elements of the third row collapse to NSN, and the entire fourth row collapses to a single NN. So your allowable outcomes are

SS

SNSS SNSN SNN

NSS NSN

NN

So your sample space consists of the 7 outcomes

{SS,SNSS,SNSN,SNN,NSS,NSN,NN}