Dependent Events

Dependent Events

How to solve dependent events problems (probability): example and its solution.


A bag is filled with 15 colored and shaped cards. A card is selected and not replaced. Then, a second card is selected. Find the probability that both cards are gray cards.

In the first selection,
the probability of selecting a gray card is 8/15.

In the second selection,
there are 7 gray cards
and 7 white cards in the bag.
So the probability of selecting a gray card is 7/14.

The probability changed
because the number of the cards have changed
and there's no replacement.

So the first selection
did affect the second selection.

Just like this case,
if the first event did affect the next event,
then those two events are called dependent events.

So the probability is (8/15)⋅(7/14) = (8/15)⋅(1/2).