Question

Parker randomly pulled out a sock that was black form

his drawer. Without replacement, what is the
probability that Parker will randomly pull out a white
sock on his second pull?

Answer 1

`Probability\ that\ Parker'd\ pull\ off\ a\ White\ Sock(\ On\ His\ Second\ Pull)=(6)/(11)`

Explanation:

`We\ are\ given\ that,\\Total\ number\ of\ Black\ Socks=7\\Total\ number\ of\ White\ Socks=12\\Total\ number\ of\ Navy\ Socks=4\\Hence,\\Total\ number\ of\ Socks\ Parker\ has=12+4+7=23\\We\ know\ that,\\The\ Random\ experiment\ here,\ is\ pulling\ out\ a\ white\ sock,\ after\ pulling\\ a\ black\ sock.\\Hence,\\Since\ the\ Black\ Sock\ had\ been\ removed\ from\ his\ drawer,\ the\\ number\ of\ 'Socks'\ that\ remain\ in\ his\ drawer=23-1=22\\`

`Hence,\\Total\ elementary\ events\ for\ this\ random\ experiment=22\\Now,\\We\ just\ need\ to\ find\ out\ the\ probability\ of\ pulling\ out\ a\ 'White\ Sock'.\\Hence,\\Number\ of\ White\ socks=12\\Hence,\\Favorable\ number\ of\ elementary\ events\ for\ the\ Random\ Experiment=12`

`We\ also\ know\ that,\\Probability\ for\ an\ Event\ A=(Favorable\ No.\ of\ Elementary\ Events)/(Total\ no.\ of\ elementary\ events)`

`Hence,\\Probability\ that\ Parker\ would\ pull\ off\ a\ white\ sock\ on\ his\\ second\ pull=(12)/(22)=(6)/(11)`