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)!
Independent
true or false ?
These are independent events; neither one depends on the results of the other.
Not necessarily. In fact, in binary situations they can be totally dependent - depends on the experiment.
They are independent, because the probability of the first event does not affect the probability of the second event.
What is the difference between dependant and independent events in terms of probability
Given two events, A and B, Pr(A and B) = Pr(A)*Pr(B) if A and B are independent and Pr(A and B) = Pr(A | B)*Pr(B) if they are not.
No, you multiply for independent events.
Two events are said to be independent if the outcome of one event does not affect the outcome of the other. Their probabilities are independent probabilities. If the events are not independent then they are dependent.
Independent
Nope.
true or false ?
Yes
These are independent events; neither one depends on the results of the other.
Whether the events are independent or dependent, whether or not they are mutually exclusive.
dependent event
when the occurance of an event B is not affected by the occurance of event A than we can say that these events are not dependent with each other