Question

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent?

Answer 1

Initially

: Pr (Pink to 1st Woman) = 4 / 15

As the first chosen flower is pink:

: Pr (Pink to 2nd Woman) = 3/14

But let's say that the 1st woman had been given a yellow carnation, then

: Pr (Pink to 2nd Woman) = 4/14

In each case, the 1st event has an effect on the 2nd event.

If it were being done "with replacement", so that each time the selected flower was to be replaced with an exact image, the it could/should be independent.

But it's not.

There are floral ways of recognising this, but yer common sense should guide you to an answer :)

the best test, usually, is this:

If \(P(A) = P(A|B)\), then A and B are independent events

Answer 2

this is a Probability question