Because the two are independent, the calculation becomes the product of the two by definition.

We need to recall that  respresents the compliment of A which is everything that is not in A or in mathematical terms:

.

Likewise for the compliment of B:

Therefore to find the intersection of these two independent events we multiply them together.

The gender of each child can be considered an independent event. Each child has a 50% chance of being a boy, and whether a boy was already born previously does not affect the next child's gender.

These two events are independent of one another. During sampling with replacement, the first card does not affect the second card being picked.

To illustrate, consider the probability of drawing a heart first

Assuming you first drew a heart and replaced it in the deck, does the probability of drawing a heart as the second card change?

The probability remains the same, there are still 13 hearts and 52 total cards.

These events are not independent, because if one event happens, it affects the probability of the other event happening. Consider the probability of drawing a heart and the probability of getting a heart given a heart was already drawn. If these two probabilities are the same, the events are independent. If the two probabilities are not the asme, the events are not independent.

After a heart has already been drawn, there are now only 52 cards total and 12 hearts left. These two probabilities are not equal, therefore the events are not independent.

Events which are mutually exclusive are dependent events. This is becauce if one event happens, it affects the probability that the other event will happen.

Example- Tonight you may attend a soccer game or a basketball game. These events are mutually exclusive because they share no overlap. However, if you go to the basketball game, it changes the probability of you going to the soccer game to zero. Therefore, mutually exclusive events are not independent.

First you find the total amount of marbles that are in the bag which is 26 ().  Then you must add up all of the marbles that are not yellow which is 19 (9 red marbles + 10 blue marbles).  Finally, you must divide the total marbles that are apart of you set (19) by the total marbles (26) and that gives you a probability of .

There are 13 men to choose from in order to make an 11 member football team. Thus, the answer is set up as: 13 choose 11: .

The answer is found by multiplying  by the probability :

 emails

The two events in this case are dependent (the result of the first event will affect the outcome probabilities of the second event). Find the probability of a particular outcome for both events by multiplying the probability of event A by the probability of event B given the result of A. In other words, multiply the probability of both events, remembering to account for the result of event A in determining the probability of event B.  Here, the probability of selecting a yellow marble the first time is 3/8, and the second time is 2/7.

This problem asks for the probability of one event or another, so the addition rule of probability is approriate. However, brown horse and female horse are not mutually exclusive events, because there are brown female horses. Therefore we must subtract the brown male horses to avoid double counting.

Now, fill in the equation.