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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
I need to calculate the probability of winning the Mega Million jackpot.
First you must choose the correct 5 numbers between 1 and 56. I believe that solution is 56!/51! 5! or The probability of 1/3,819,816
The next step is, in a separate single drawing, choose the correct number between 1-46. So there is a 1/46 chance of picking that number.
is the probability of choosing all numbers 1/3,819,816 x 1/46?
How many possible outcomes of tossing a coin and rolling a 6-sided number cube?
There is 2 outcomes for flipping the coin, and 6 outcomes for rolling the cube. The total outcomes for both are 2*6 = 12.
If you flip a coin 8 times how many possible outcomes are there?
The following notes answer the above question completely and neatly. It's better in maths to try to keep it simple.
Looking at the different possible outcomes; let H = Head and T = Tail. Then the different possible outcomes are (8H +0T) meaning 8 Heads and Zero Tails, or (7H + 1T) or (6H + 2T) or (5H + 3T) or (4H + 4T) or (3H + 5T) or (2H + 6T) or (1H + 7T) or (0H + 8T) giving 9 different outcomes (possibilities).
The 9 different outcomes are not equally probable, (8H + 0T) and (0H + 8T) are the least likely while (4H + 4T) will be the most likely. However, totaling all possible outcomes there are 256.
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There are 256 possible "histories" of the whole session, corresponding to
the number of possible values of one binary 'byte', where each flip fills in
one bit of the byte.
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Another Answer:
As is usual in science, the answer depends on how you look at the problem, and on your definition of the terminology that you use. Nine different outcomes, as described above, is correct when you decide to consider only distinguishable or, more, correctly, combinatorial, outcomes.
However, in statistics and probability, we don't usually deal with combinations, we deal with permutations, because looking at permutations allows you to see the indistinguishable outcomes, outcomes which do, in fact, affect the probability of the result.
In this case, throwing a coin 8 times (or with identical results, throwing 8 coins one time), there are multiple permutations that yield the same combination. For instance, there are eight permutations of one coin being heads, there are 28 permutations of two coins being heads, and so on and so forth, leading up to a grand total of 256 different permutations of 8 coins, yielding "only 9 outcomes".
So, in summary, there are 9 distinguishable "outcomes", or combinations, while there are 256 indistinguishable "outcomes", or permutations.
(To clarify "indistinguishable", I should say that you could certainly mark each coin with a number, say from 1 to 8, and then you would be able to distinguish the outcomes or heads or tails as a function of which coin was thrown. Similarly, throwing only one coin at a time, you could write down the outcomes as they occur, and they would certainly be "distinguishable". In this context, "indistinguishable" simply means that, in the absence of some tracking system, a throw, for instance, of HTTTTTTT, or THTTTTTT, would not be different - they would both be counted as (1H + 7T), using the notation of the earlier answer.)
Now, to nail this down for completeness sake, because the answer does matter, even though the question did not ask it, take a look at probability...
Probability is simply the number of permutations of a desired result divided by the number of permutations of all results. Since there is one permutation of no heads (0H + 8T), the probability of no heads is 1 in 256, or about 0.00391. On the other hand, since there are 8 permutations of one head (1H + 7T), the probability of one head is 8 in 256, or about 0.0313. Going one more step, the probability of two heads is 28 in 256, or about 0.109.
Understanding the distinction between combinations and permutations, and distinguishable versus indistinguishable, is key to understanding probability.
What is the middle number between 29 and 35?
The number between 29 and 35 would be 32. This is 3 above 29 and 3 below 35.
First: it's not "twirl a pen", it's pen spinning. and there are many different tricks.
Second: join upsb.info it's a pen spinning forum
Third: you could also search for ktrinh93 's videos for tutorials
Forth: if you're gonna get a modded pen, please dont get a buster, beginners should not spin busters, you'll improve too fast and when you spin an mx or bictory later, you'll fail (usually)
GL fellow spinner :D
There are 26 total marbles. We will call x the number of blue marbles. So there are x+2 red marbles. If you add them together you get x + x + 2....and all that equals 26 (subtract 2 from each side and add the two x's together) 26 - 2 = x + x 24 = 2x then divide each side by two and you get 24/2 = 2x/2 simplified is 12 = x So x is 12 (blue marbles) and x + 2 is 14 is (the amount of red marbles). 12 + 14 = 26!
Probability of an event occurring to the probability that it won't occur?
These events are complementary. Let P(A) = probability event will occur. Then the probability it will not occur is: 1 - P(A).
Does a sample statistic always have a normal distribution?
No, many sample statistics do not have a normal distribution. In most cases order statistics, such as the minimum or the maximum, are not normally distributed, even when the underlying data themselves have a common normal distribution. The geometric mean (for positive-valued data) almost never has a normal distribution. Practically important statistics, including the chi-square statistic, the F-statistic, and the R-squared statistic of regression, do not have normal distributions. Typically, the normal distribution arises as a good approximation when the sample statistic acts like the independent sum of variables none of whose variances dominates the total variance: this is a loose statement of the Central Limit Theorem. A sample sum and mean, when the elements of the sample are independently obtained, will therefore often be approximately normally distributed provided the sample is large enough.
The probability of pulling a red or yellow marble out of a bag of 3 green 8 red 8 yellow and 3 black marbles is 16 out of 22, or about 0.73.
symmetrical :)
i do believe!
hope this helps!
Pixie
x
Suppose the variance is 64 Find the standard deviation?
Standard deviation is the square root of the variance; so if the variance is 64, the std dev is 8.
The Associative Property does not work for which operations?
Subtraction and division.
While 2+ (3+4) = 2+ (4+3), the subtraction 2-(3-4) ≠ 2-(4-3). One yields 3 while the other yields 1.
Similarly, multiplication has this property while division does not.
1% total
0.5% in either direction
What is the advantages of random sampling?
Please read related link on what defines a simple random sample. When a sample is done randomly, then every item in the population has an equal chance of being selected. An advantage of random sampling is unbiased statistics. An unbiased statistic has the characteristic that as the sample size increases, the statistics from the sample approaches the true values of the population. This is true if the probability distribution of the population is not changing with time, or as a result of being sampled. Using a random sampling method does not guarantee statistics free of bias. For instance, if I wanted to produce a biased result, I might ask loaded questions. I might also pick particular city, say Chicago, and ask people at random for their favorite team. Obviously, my statistic is not valid outside of Chicago. A second advantage is that the statistical analysis related to sample distributions, hypothesis testing, and sample size determinations assume that the sample is a simple random sample. Remember. the goal of all sampling methods is to obtain information that is representative of the population that is under study. It may not be practical to do a random sample in many cases. For example, suppose I want to know how many people die before age 45 in the world. My random sample would have to include people any country. You can find more information on random sampling and other methods by searching under random sampling methods.
How many outcomes are possible if a coin is tossed 15 times?
If a coin is tossed 15 times there are 215 or 32768 possible outcomes.
Is it possible to have a probability greater than 100?
It is not possible to have a probability greater than 1. All probabilities are between 0 and 1, inclusive.
What is the probability of randomly selecting a heart from a standard deck of 52 card?
There are 13 hearts in the standard deck, A-10,J,Q,K. So your probability is 13/52 which is 1/4 or 25% chance
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A number from 0 to 1 that describes how likely an event is to occur?
This would be a probability factor.
A multiple choice question has has 5 choices What is the probability of guessing it correctly?
There is 1 right answer out of 5 possible answers, so the probability of guessing it correctly is 1/5 or 20% or 0.2.
What is the distribution of area under a curve?
In terms of probability theory, the cumulative distribution function (cdf) is the result of the summation or integration of the probability density function (pdf). The cdf F(a) is the area under the pdf from its lower limit to a. I hope I am responding to your question. If not, perhaps you can clarify it and resubmit it.
The variance for the binomial probability distribution is?
n(p)(1-p) n times p times one minus p, where n is the number of outcomes in the binomial distribution, and p is the probability of a success.
Are the ages of people in the united states normally distributed?
No. Ages of people dicrease as the age increases - not just in the US but in all countries.
Calculate the Z value and determine the area (probability) between the Z values. Z = (x-mu)/sigma. Z42 = (42-50)/4 = -2 & Z68 = (68-50)/4 = 4.5. Go to the related link and the areas are .0228 & for 4.5 use .9999. Subtract the two values; .9999 - .0228 = .9771.
