What is the sample space for this situation.

Question

A telephone sales representative makes successive calls to potential customers, and the result of each call is recorded as a sale (S) or a no sale (N). Calls are continued until either two successive sales are made, two calls result in no sale (these calls need not be consecutive), or a total of 4 calls is made. 

Answer 1

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}