Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B

FOR THE FIRST BUCKET ...

Red color - 2

Blue color - 2

FOR THE SECOND BUCKET

Red color - 3

Blue color -2

In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :

Scenario I - He picks Red color from List A and Blue color from List B

Scenario II - He picks Blue color from List A and Red color from List B

Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5

Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...

Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...

We get 1/5 + 3/10 = 1/2 (B)

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"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas