Consider first all of the possible ways the men may be arranged, which is

Now, consider all of the ways that Aaron and Gary could be seated beside each other; it may be easier to visualize by drawing it out:

1. A G _ _
2. G A _ _
3. _ A G _
4. _ G A _
5. _ _ A G
6. _ _ G A

As seen, there are six possibilities.

Finally, for each of these cases, Craige and Boone could be seated in one of two ways.

So the probability that Aaron and Gary will be seated beside each other is:

A coin only has two outcomes, heads or tails.  So if the coin is flipped "t" times, "h" of those times are heads and "t-h" of those times are tails.

From here, we use the simple probability formula:

sowe simply create a fraction that has the number of tails-up divied by the total number of flips;

The probability of any given event is given by the equation 

P= [(number of desired events) / (total possible events)] x 100%

In this example, let x represent the number of blue skirts. 

If there's a 25% probability that the skirt Sarah chooses is blue, then the probability of the event can be written like this:

P = (x/12)(100%) = 25%

To solve for x, we can set up a proportion like this:

By cross-multiplication, we get

Therefore, x=3. 

In order to find the probability of the outcomes that Jennifer, James and Kensington flip, you need to multiply the probability of each outcome by each other. 

The probability of the outcome of an event is given by the number of desired outcomes divided by the total number of possible outcomes. 

For this example, since there are three blue scarves, there are three desired outcomes. In total, there are seven possible outcomes—one for each scarf Amelia could pick. 

Therefore, the probability that she will pick a blue scarf is . 

The probability of spinning an A is . The probability of spinning an B is also , and the same goes for spinning a C.

To find the probability of spinning an A, B, or C, we simply add these individual probabilities together. 

Remember that we can find the probability of an event by dividing the number of possible desired outcomes by the total number of possible outcomes. 

Since Robert has already pulled out the queen of hearts, that means that there are 51 cards remaining in the deck. That also means that there are only 3 queens left. 

With this in mind, Rebecca pulls out a card from a deck of 51 total cards (the total number of possible outcomes), 3 of which are queens (the desired number of outcomes).

Therefore, the probability of her pulling out a queen is . 

The probability of an event is given by dividing the number of desired outcomes by the number of total outcomes. 

Because each roll is an independent event, that means that the probability of rolling a second six is the same as rolling the first six. 

The probability of rolling a six (one desired outcome) on a standard die (six total possible outcomes) is . 

Given two events, the following rule is true:

Therefore, 

Step 1: Find the probability of getting only one color. We will denote probability of red as , probability of blue as  and green as . 

.

This fraction cannot be simplified anymore. The numerator is divisible by 2 and the denominator is not divisible by 2.

Step 2: We need to find the probability of getting 1 red and 1 blue. We need to use a formula: , where  and .

Step 3: Using the formula in step 2, substitute  and  into the equation and multiply. 


We get: 

So, the probability of getting a red and a blue marble is .