Compare probabilities of independent and probabilities of dependent events.
Any examples???
Independent is by itself. Dependent needs a problem before it.
Okay, so like 14 is independent, and
7 + 7 = 14???
7+7=14 is dependent?
Yes, as long as the equation is not rationalized.
Certainly! Let's start by understanding the difference between independent and dependent events.
Independent Events:
In probability, independent events are those where the outcome of one event does not affect the outcome of another event. The probability of an independent event occurring is calculated by multiplying the probabilities of each event.
For example, let's say you are rolling two fair six-sided dice. The probability of rolling a 3 on the first die is 1/6, and the probability of rolling a 4 on the second die is also 1/6. Since these events are independent, the probability of rolling a 3 on the first die AND a 4 on the second die is (1/6) * (1/6) = 1/36.
Dependent Events:
On the other hand, dependent events are those where the outcome of one event does affect the outcome of another event. In this case, we need to adjust the probability calculations accordingly.
Let's consider an example. Suppose you have a bag with 4 red marbles and 3 green marbles. If you draw one marble randomly and without replacement, the probability of drawing a red marble on the first draw is 4/7. Now, let's assume that you do not replace the first marble back into the bag. For the second draw, the probability of drawing a red marble depends on the outcome of the first draw. After the first red marble is removed, there are now 3 red marbles left out of the remaining 6 marbles. Thus, the probability of drawing a red marble on the second draw is 3/6. The overall probability of drawing two red marbles in succession is (4/7) * (3/6) = 2/7.
To summarize, when events are independent, the probabilities are multiplied, whereas in the case of dependent events, the probabilities are adjusted based on the outcomes of previous events.