The number of balls placed in the box will be 

The sum of the first  natural numbers is 

, 

so there are

,

balls in the box.

"M" is the thirteenth letter of the alphabet, so thirteen balls are marked with an "M". The probability of drawing this letter is

The probability that the spinner will stop in a red sector depends on the angles of the different colored sectors, not on the sizes of the sectors. The radii of the sectots is therefore irrelevant.

Each red region is half of a quarter-circle, so the two sectors are, together, one fourth of a circle. The odds against the spinner stopping in a red circle are therefore three fourths to one fourth, or 3 to 1, against.

An unaltered standard deck of 52 cards contains 13 of each of the four suits. Switching a spade and a club from this deck with a spade and a club from another deck yields an altered deck, but with the same number of cards, and with the same number of cards of each suit. No probabilities changed.

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 .