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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
2 dice are rolled find the probability of getting exactly 2?
Each die can come up in 6 ways.
You get exactly 2 only if both dice come up as a ' 1 '.
The probability of the first one coming up '1' is (1/6).
The probability of the second one coming up as a '1' is (1/6).
The probability of both coming up as '1' is (1/6 x 1/6) = (1/36) = 2.78% (rounded)
The probability when you roll two dice that you roll an odd number on the first die and a 1 on the second die is 1 in 12.
The two die are sequentially unrelated, so you can consider them separately. The probability of rolling an odd number is 3 in 6, or 1 in 2. The probability of rolling a 1 is 1 in 6. Multiply the two probabilities together and you get 3 in 36, or 1 in 12.
How do you find the probability of a fraction and a whole number?
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.
How does random assignment in experiments differ from random sampling in surveys?
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.
What is the standard error if the population standard deviation is 100 and the sample size is 25?
Formula for standard error (SEM) is standard deviation divided by the square root of the sample size, or s/sqrt(n). SEM = 100/sqrt25 = 100/5 = 20.
What is the probability a girl is chosen if 15 students are girls and 10 students are boys?
The ratio of girls to total students is 15:25, or 3:5. Three out of five students are girls so there would be a 60% probability that a girl would be chosen; a 2 out of 5 chance, or 40% probability that a boy would be chosen.
Isotherm
Consider a surface:
Definition:q0, q1, ..., qn = Surface area (cm-2) covered by 0, 1, ..., n layers of adsorbed molecules.
At Equilibrium:q0 must remain constant. . Rate of Evaporation Rate of Condensation . . = from First Layer onto Bare Surface
Similarly, at equilibrium q1 must remain constant. . Rate of Condensation Rate of Condensation . . on the Bare Surface on the 1st Layer + = + Rate of Evaporation Rate of Evaporation from the second layer from the second layer . . . k1Pq0 + k-2q2 = k2Pq1 + k-1q1
Substituting into (I) gives
k-2q2 = k2Pq1
Extending this argument to other layers,
Definitions:
Total surface area of the catalyst,
Total volume of gas adsorbed on surface
where v0 is the volume of gas adsorbed on one square centimeter of surface when it is covered with a complete layer. . . .
where vm is the volume of gas adsorbed when the entire surface is covered with a complete monolayer.
From (I),
If we assume that the properties of the 1st, 2nd, ... layers are equivalent, then,
Similarly,q3 =xq2 =x2q1
Generally,qi =xqi-1 =xi-1q1 =xi-1yq0 =cxiq0 {c=x/y}
Substituting into (V),
Now,
Also, . . .
At saturation pressure of gas P0, an infinite number of adsorbate layers must build up on the surface. From equation VII, for this to be possible,
must be infinite. This means that at P0, x must equal 1. . . . g = P0(From definition of x) . . . x = P/P0
Substituting into VII, we arrive at the recognized form of the BET isotherm,
This can be rearranged to give,
What are Advantages and disadvantages in multistage sampling?
Advantages are:
1. Fewer investigators are needed
2. It is not so costly to obtain a sample
Disadvantages are:
1. There is the possibility of bias if, for example, only if a small number of regions are selected
2.The method is not truly random as once the final sampling areas have been selected the rest of the population cannot be in the sample.
If the population is heterogeneous, the areas chosen should reflect the full range of the diversity. Otherwise, choosing some areas and excluding others (even if it is done randomly) will result in a biased sample.
If you toss a coin 5 times how many outcomes are there?
For a coin toss, there are 2 possible outcomes (heads or tails). For five tosses, therefore, there are 25 possible outcomes (25 = 32). However, this assumes that order is important (i.e. that HtttH is different to tHtHt). If you don't care what order the heads or tails fall in, there are only 6 outcomes.
What is the probability of prime numbers being chosen randomly from the number 1-49?
15/49
Explanation
There are 15 prime numbers between 1 and 49 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47). If you randomly choose one natural number from the 49 numbers between 1 and 49 inclusive, there is a 15/49 probability that it will be prime.
What is the probability that a penny will land heads up?
The probability of heads is 0.5 or 1/2. This is wrong, the chances of a penny landing heads up is less than 0.5 because the cast in Lincoln's head weighs more than the tails side of the peeny.
decreases
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
Two dice are rolled what are the odds against a sum greater than 8?
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.
What are the odds of rolling a 3 4 times in a row?
The probability of rolling a 3 on a die are 1/6. Since each roll is an independent event, the probability of rolling a 3 4 times in a row is (1/6)4 or 1/1296.
The odds of something happening are the chances of it happening vs. the chances of it not happening. The chance of not rolling a 3 4 times in a row is 1-(1/1296) or 1295/1296.
Therefore the odds are 1:1295
What is linear snowball sampling?
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.
If you flip a coin 5 times what is the probability that the results are all heads or all tails?
The probability of getting all heads or all tails in 5 flips of a coin is 1 in 16.
The probability of getting a head or a tail on the first flip is 1 in 1. The probability of each of the following coins matching the first coin is 1 in 2. Simply multiply the five probabilities (1 in 1) (1 in 2) (1 in 2) (1 in 2) (1 in 2) and you get 1 in 16.
It is true that the probability of getting all heads is 1 in 32, and the probability of getting all tails is also 1 in 32. Since the question asked the probability of both cases (all heads or all tails), the answer is 1 in 16.
