Difference between independent and dependent events?

Answer 1

Two events are independent if the outcome of one has no effect on the

outcome of the other. The classic example would be rolling a pair of

dice. What happens with one die has no effect on what happens with the

other die.

Two events are dependent if the outcome of one has an effect on the

outcome of the other. The classic example would be drawing cards from

a deck without replacement. The probability of drawing an ace changes

depending on what other cards have already been drawn.

Probabilities for independent events often involve exponents, while

probabilities for dependent events often involve factorials.

How many ways are there to roll three dice? There are 6 ways to roll

the first, 6 ways to roll the second, and 6 ways to roll the third, so

the number of possible outcomes is

6*6*6 = 6^3

How many ways are there to draw three cards from a deck without

replacement? There are 52 ways to draw the first one; but now there

are only 51 ways to draw the second (because one card has been

removed); and only 50 ways to draw the third. So the number of

possible outcomes is

52 * 51 * 50 = 52! / (52 - 3)!