Probability

Given any number it is easy to find a rule based on a polynomial of order 5+k such that the first five numbers are as listed in the question and the next k are the given "next" numbers.

However, use the rule

Un = (-6n4 + 83n3 - 411n2 + 874n - 468)/6

Accordingly, the next three numbers are 22, -71, -310

It is 1/12.

8 in 52

Let the number of sweets be n and use the rules of probability:-

If: 6/n times 5/n-1 = 1/8

Then: 30/n2-n = 1/8

Multiplying both sides by n2-n: 30 = n2-n/8

Multiplying both sides by 8: 240 = n2-n

Subtracting both sides by 240: 0 = n2-n-240

Solving the above quadratic equation: n = 16 or n = -15

Therefore it follows: n = 16 sweets

Note that n2 means n squared

Earth

The answer will depend on what the experiment is.

Ketchup

Although it's not clear which distribution you're referring to, I sense that I know what you mean. This is one of those situations where a function is only asymptotically zero, which is to say that it reaches zero only in the limit. But, no matter how large the exponent is, it never actually reaches zero; therefore, the probability never becomes zero. It only becomes extremely small.

Yes. It should reduce the variance.

7.7% or 4/52

6/7

No.

If they can all be distiguished from one another, then 8*2 = 16 ways.

8.5%or 8 1/2%

That would depend on the conditions of the experiment.

50%

Yes.

There are (1*5*4)*(3*2*1) = 120 arrangements.

It is 15/50 = 0.3

55mph

The probability is 1. If the maximum number of hairs is 100000 then there can be only 100000 people, each with a different number of hairs: 1, 2, 3, ..., 100000. Then the 100001st person must have the same number as someone in that list. Since the population of NYC is greater than 100001, then the event is a certainty.

A good red black deck has a lot of creatures that deal lots of damage. The black portion of the deck should have some zombies and other undead stuff. The red portion should be able to boost power and deal a lot of damage

2234.

4C2(1/2)4 = 6/16 = 3/8