Probability

12/27 reduces to 4/9

numerator = the number of acceptable outcomes

denominator = total number of outcomes (12 boys + 15 girls)

four out of seven times

For ease of answering, we will work under the assumption that the probability of someone being born within any given month is equal to that of any other month.

Allowing that assumption, we can look at that question a slightly different way and say "What is the probability that all people in a group of six would each be born in a different month?" The answer to that would be 12/12 * 11/12 * 10/12 * 9/12 * 8/12 * 7/12, which can also be expressed as (12! / 6!) / 126, and comes out to 665280 / 2985984, which equals 385 / 1728.

The probability of at least two being being born in the same month would then be:

1 - 385 / 1728

= 1343 / 1728

≈ 0.7772, or approximately 77.72%

3

representative

15 trials: 3 times

40 trials: 8 times

75 trials: 15 times

120 trials: 24 times

But don't bet on it.

Assuming it is a 6-sided number cube, it would be 6.

7 out of 25 times

Standard deviation shows how much variation there is from the "average" (mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

4/6, 5/5, 5/6, 6/4, 6/5, 6/6 ie 6 out of 36.

7

19

T r+1 = (n / r) (a ^n-r) x (b)^r

standard deviation

If there are four possible answers to a question, then a guessed answer would have a probability of 1 in 4. If there are six questions, then the mean number of correct answers would be six times 1 in 4, or 1.5

Many interesting coincidences have been observed, relating to the number 23 (the late Robert Anton Wilson wrote about this at some length, and of course there is even a movie about it) but there are also lots of interesting coincidences concerning many other numbers, and chances are, something notable can be observed about practically any number you come up with. We are always counting things and attaching numbers to things, everything happens at a specific time that can be described by a number, and a specific place that has an address, and involves a specific number of people and objects, having specific weights, speeds, monetary worth, and various other factors all of which can be described by a number; there are endless opportunities to find numbers and to find coincidental relationships between numbers. Consider the fact that in the radio comedy program (later made into novels, a TV series, and a movie) called "The Hitchhiker's Guide To The Galaxy, Douglas Adams suggested that the ultimate answer to life, the universe, and everything is 42. This was a joke, however, many people heard or read this, and started looking more closely at the number 42, and guess what, there are all sorts of interesting coincidences involving the number 42. It works just as well as the number 23. And it was chosen at random.

Simplest terms, it means that the sample values are grouped closely together. Another way of saying it is that the range of values is small.

The plot will be a leptokurtic plot (peaked).

In geology say, a gross sample would be a representative sample of the whole rock. A lab sample would be a fraction of that, refined such that measurements are able to be made on a single mineral.

for example, a piece of basalt would be a convenient field (gross) sample, from which say, mica is extracted after grinding and separation, to enable the 'date' of the basalt to be determined.

Similar concepts would apply in other fields, such as biology, botany, water sampling and so on.

Tree diagram

The probability that a spinner with N sides stops on 2 particular numbers in two spins in 1 in N2. It does not matter what the two numbers are, since the two spins are sequentially unrelated.