Independent Events

Independent Events

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

Example

A bag is filled with 15 colored and shaped cards. A card is selected and 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,
the probability of selecting a gray card is also 8/15.

The probability didn't change
because of the replacement.

So the first selection
didn't affect the second selection.

Just like this case,
if the first event didn't affect the next event,
then those two events are called independent events.

So the probability is (8/15)⋅(8/15).