In a store suppose that there are 4 green chairs 6 green tab

In a store, suppose that there are 4 green chairs, 6 green tables, and 6 red chairs. How many red tables must be present if color and furniture (chair/table) are to be independent when furniture is selected at random? Explain your answer!

Solution

We need the proportion of green chair with green tables same as red chair with red tables so that no matter color is chosen, P(chair) is same.

Thus 4/6 = 6/x => x = 9

Thus we should have 9 red tables.

Apparently this approach stores independence in other direction too, P(red) is also same for chairs and tables