Probability

If you have three DIFFERENT letters, you can arrange them in 3! = 1 x 2 x 3 = 6 different ways.

13, if you want to be sure. It's impossible for a group of 13 people not to have at least one pair that share a birth month, because there are only 12 months.

If you'll settle for a lower probability, thechance that a group of 5 randomly chosen people will contain at least one pair born in the same month is about 3/5, and if you gather 6 people the chance that at least two of them will share a birth month is about 4/5. Those aren't exact probabilities both because the math doesn't work out that way and and because birthdays are not randomly distributed by month ... significantly fewer people are born in February than in August. An exact probability would need to take that into account, and it's frankly more research and math than I want to do unless I'm getting paid for it.

1/3

A deck of cards consists of 52 cards.

Each card is available four times.

That makes 13 diffent card types.

Four different cards are worth 10 points: 10, Jack, Queen, King.

That means that 4x4 Cards out of 52 are worth ten.

That are about 30% (30/100).

Two tens in a row have the expectation of 30%x30% which is about 9%.

At most 5 means 0, 1, 2, 3, 4, or 5.

4

The number of ways that 15 books can be arranged on a shelf is the same as the number of permutations of 15 things taken 15 at a time. This is 15 factorial, or 15!, and is 1,307,674,368,000.

Never, because there is no such distribution.

Spades.

It is 1/(2^4)

i.e. 1/16

This is because there is 1 in 2 chance of it happening once, and multiply by itself for each successive go.

About 1 in 3.

There are several ways to determine p, the probabilityof success. First is by trials, called relative frequency. Second, use the classical approach which is calculate how many times it can occur divided by the sample space. Third is subjective, an educated guess.

pot of greed,heart of the underdog,

Yes.

All pairs are only half as likely. This is because a set of different faces can have either die showing one of the values and the other showing the other.

Thus, 2-2 will only happen if both, die A = 2 and die B = 2

But 2-3 will happen if A = 2 and B = 3 OR if A = 3 and B = 2.

nobody knows

It means that it could rain

3 to 1

The probability of getting a perfect score in a three-question true or false quiz is 100% if you studied and retained the subject matter and the questions addressed that subject.

If, however, you did not study, and you made pure guesses without any bias towards an answer partially based in your (now rather poor) knowledge, then the probability of getting any one question correct is 50%, so the probability of getting all three questions correct is 50% to the third power, or 12.5%.

As long as the 124 just sits there without having anything done to it, there are no outcomes.

1st dice = 6 possibilities

2nd dice = 6

3rd dice = 6

Coin = 2

Total = 6x6x6x2 = 432 outcomes

The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities.

However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference.

The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.

It depends on whether you are playing poker or baccarat (21).