It would be different if Yahoo users used Yahoo because Yahoo uses Bing, but that's not the case. For example, Bing gets used in some searches because they cut Yahoo a good deal, and Yahoo pays Firefox to be the default search provider. That has nothing to do with Bing's search quality.
http://venturebeat.com/2015/04/15/comscore-bing-steals-from-...
http://searchengineland.com/google-controls-65-percent-of-se...
And 30%+ with Yahoo.