Probability

That depends what you mean. If you mean finding the product of a fraction and a whole number, simply multiply the numerator of the fraction by the whole number and reduce to its simplest form.

For example, 3/4 x 4 = 12/4, which, when reduced to its simplest form, is equal to 3.

C(8,3) = 56

Random sampling in surveys takes a randomly selected smaller group from a larger population (so the smaller group is a sample of the larger group). Random assignment separates (randomly) this chosen small group further, into a control group and a treatment group for experiments. For instance, in research surveys: if a group of sick people are asked about their symptoms, they are placed in separate categories of similar symptoms, and then are diagnosed with particular illnesses. Further, in random assignment: if one medicine is given to the group, and it only helps certain symptoms, then a cure has been found for only those particular illnesses, and not the others. You see, random sampling asks certain questions of subjects and gets various responses, whereas, random assignment applies certain principles to subjects and gets various responses. Both ways lead to results which render solutions to problems. If not, further experimentation needs to be made.

It's not supposed to be.

If it is, then the dice are referred to as "loaded", and using them in a game

can be hazardous to your health.

The probability of rolling a sum of 8 with two dice is 5 in 36 or about 0.1389.

2 and 6

3 and 5

4 and 4

5 and 3

6 and 2

This is a non-random sampling technique where the initial respondents to a survey recruit others for a survey.

Linear snowball sampling is when the first responent recruits one more person for the survey, who in turn recruits one more person for the survey. Number of people surveyed will increase in a linear manner.

The related links provide good discussion of this form of surveying. It is a non-representative sample, but it is an effective means of surveying people with common traits who might otherwise be difficult to find.

For example, I want a statistical profile of people that are "hackers" so every hacker I find, I would ask if I could interview his "fellow hackers."

See related links.

Well each dice has the possibility of 6. So the highest number would be 12. 12, 11, 10, and 9 are higher than 8.... And odds against means the # of unfavorable over favorable. So... Unfavorable would be 7 #'s and favorable is 5 so it would be 7/5.

C(7,2)*(.9)^5*(.1)^2, or about .124 = 12.4%

For the desired outcome, considering the seven patients, you need:

(Survive,Survive,Survive,Survive,Survive,Die,Die)

(Survive,Survive,Survive,Survive,Die,Survive,Die)

(Survive,Survive,Survive,Die,Survive,Survive,Die)

.

.

.

(Die,Die,Survive,Survive,Survive,Survive,Survive)

There are C(7,2) [the number of combinations of 7 things taken 2 at a time] = 21 possible desired outcomes. The probability of each of these outcomes is (.9)*(.9)*(.9)*(.9)*(.9)*(.1)*(.1). Multiplying 21 by (.9)*(.9)*(.9)*(.9)*(.9)*(.1)*(.1) yields the answer.

True.

1/9 ways. total sample space for the experiment is 36(because you have two dice). and you can get 5 in 4 ways that is (1,4),(4,1),(2,3),(3,2). hence 4/36= 1/9.

The sample space of a standard six sided die is [1,2,3,4,5,6].

1.14

Less. The more times the coin is tossed, the more likely it will reflect the actual odds of .5 heads and .5 tails.

Sum of all probabilities is 1.

(2,6),(3,5),(4,4),(5,3),(6,2)=5/36

the stem and the responses

CHOICES

among the responses.

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.

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