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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
What are the odds of rolling a four 3 times in a row using two dice?
Assuming fair dice:
With 3 dice there are 6 x 6 = 36 possible permutations (the two dice can be identified and are independent of each other).
Of these there are 3 ways (1+3, 2+2, 3+1) of getting four.
Probability of getting a four with 2 dice on one roll = 4/36 = 1/9
As rolls are independent, the probability of getting 4 with 2 dice 3 times in a row is 1/9 x 1/9 x 1/9 = 1/729
So the odds of it are 728 to 1 against, ie 1 in 729 or about 0.14 %.
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91
How do you calculate the probability for a group of several independent events?
You multiply together their individual probabilities.
How many 5 letter combinations can you make with the vowels?
There are five vowels. Notice that any of the vowels could be chosen from 0 though 5 times in any given combination. We therefore need the number of combinations of 5 from 5 _with replacement_.
This is the number ( 5 + 5 - 1 ) choose 5 = 126.
Why does a 10 sided dice have 9 for the highest number?
Ten-sided dice are often used in games that require a "percentage roll", such as Dungeons & Dragons. Players roll two 10-sided dice, and the numbers rolled are used as digits to form a number between 0 and 99. Using a "0" instead of "10" simplifies this process.
For most other games and instances, zeroes on ten-sided dice represent tens.
Just FYI - some ten-sided dice do actually have a "10" instead of a "0", but they're fairly rare. I got 4 of them in a board game called Filthy Rich, which - ironically enough - uses numerous references to rolling zeroes instead of tens. Go figure.
Is the binomial distribution is a continuous distribution?
No it is a "discrete" distribution because the outcomes can only be integers.
How many ways to arrange the letters abcd?
4 choices for the first letter
3 choices for the second, once the first has been chosen
2 choices for the third, once the first and the second have been chosen
1 for the last
So it's 4x3x2x1 = 24
How is it that the Mean of a set of values is related to the Standard Deviation of that set?
If you're in a hurry, then skip to the end, but know that this explanation is very thorough, and may help you remember why the relationship is what it is. Remembering that will help you to remember the relationship itself, and will even help you to derive that relationship if you should forget it.
The Mean is the average value of a set of values, found by dividing the sum of all values in the set by the total number of values in the set.
For example, the average of the set of 5 numbers, {13, 17, 15, 16, 20}, would be (13+17+15+16+20) divided by 5, the total number of values in the set.
That would be 81 divided by 5, which would be 16.2.
Thus, the average value of the numbers in the set is 16.2, even though none of them is exactly 16.2.
To find the Standard Deviation, you need the average value of the numbers in the set (the Mean), as well as the total number of values in the set, and the values themselves.
Because the Standard Deviation is the average distance of the actual values from the Mean, we must first find the Difference between the actual values and the Mean.
We do this by subtracting the Mean from each of the actual values, but, because some of the actual values are lower than the Mean, this will produce some negative numbers, and, if you think about the Difference as Distance, then you will realize that the Differences should not be negative, as Distance cannot be negative.
13 - 16.2 = -3.2
17 - 16.2 = 0.8
15 - 16.2 = -1.2
16 - 16.2 = -0.2
20 - 16.2 = 3.8
The Standard Deviation would be artificially narrowed if you calculated the average Difference between the actual values and the Mean using negative Differences, because the negative Differences would cancel out the positive Differences, so that when you calculated the average Difference, your numerator, the sum of distances from the Mean, would be artificially small.
If we tried to treat negative Differences the same way that we treat positive distances, we would see that something goes horribly wrong. The negative Differences completely cancel out the positive Differences, leaving us with zero.
(-3.2) + (0.8) + (-1.2) + (-0.2) + (3.8) =
(0.8) + (3.8) + (-1.2) + (-0.2) + (-3.2) =
0.8 + 3.8 - 1.2 - 0.2 - 3.2 =
4.6 - 4.6 = 0
This makes sense, because the Mean is basically the point around which all actual values in a set are balanced.
The fact that some Differences are negative only confirms that some values in the set are lower than the Mean, and others are greater than the Median.
In this case, the negative signs indicate direction, but distance itself is always positive, so we need to find a way to make all of these Differences positive.
13 - 16.2 = -3.2
17 - 16.2 = 0.8
15 - 16.2 = -1.2
16 - 16.2 = -0.2
20 - 16.2 = 3.8
We find that we are able to do this by squaring the original Differences, as the square of any real number is always positive.
(-3.2)2 = 10.24
(0.8)2 = 0.64
(-1.2)2 = 1.44
(-0.2)2 = 0.04
(3.8)2 = 14.44
We now have the positive squares of the Differences, and so we can now find the average of those squares by adding them and then dividing their sum by the number of values in their set, which is the same as the number of values in the original set, which, in this case, is 5.
10.24 + 0.64 + 1.44 + 0.04 + 14.44 = 26.8
26.8 / 5 = 5.36
Remember that we had to square the Differences in order to have positive numbers to work with, so, what we have here is the average squared Difference between the values of the original set and the Mean. Therefore, in order to find the average Difference, we must take the square root of the average squared Difference.
SQRT (5.36) = 2.3152
This gives us the average distance between values in a set and the Mean of that set, and we know that distance to mean the same thing as the Standard Deviation, so, the Standard Deviation in this example is 2.3152.
In short, the relationship between the Mean and the Standard Deviation can be expressed as follows:
The Standard Deviation is the Square Root of the Average of the Squares of all the Differences between values in a set and the Mean of that set.
SQRT ( ( (V1 - Mean)2 + (V2 - Mean)2 + ... + (Vn- Mean)2 ) / (n) )
SQRT = take the Square Root of the following expression in parentheses
V = a value in a set, such as, the 1st, 2nd, and nth value in a set
n = the number of values in that set
How do you calculate sample size?
Count up the number of obseravtions made on the experimental units. That is the sample size.
How many ways to arrange the word corporation?
Word "CORPORATION" has got 11 letters so we could arrange 11 letters in
11P11 ways=11! ways
But, Letter 'O' and 'R' are repeating thrice and twice respectively.
And, presence of duplicates reduces the chances of possible arrangements.
Hence it will become, 11!/(2!*3!) [Since 'R' and 'O' are repeating twice and thrice respectively]
Why are the sum of the opposite face of die is 7?
Because the put the opposite #'s on the opposite side
Which of the following is an example of thoretical probality?
there are 52 playing cards in a deck and 4 of them are aces. the probability of turning over an ace is 4 over 52.
Which of these events occur when you walk out into the cold?
The most important way of preventing frostbite is to get out of the cold.
When rolling a number cube twice what is the probability of rolling the same number each time?
1 out of 6, if the highest number on the cube is 6. hope that helped!:)
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If only rolling ONE 6-sided die, and it can be any first roll that is matched by the second roll, the odds would be 1 in 6. It would not matter what the 1st roll came up with, so 6 in 6 rolls meet the 1st criteria. But the second roll could be any of the six sides, and only one of them would match whatever the number rolled first was.
If however, rather than a cube you used a differently shaped die, with a different number on each of its faces, the odds would be one in however many sides the die has.
When tossing 2 dice the problem can be more difficult to compute if satisfied by the total to be matched, or if the exact same #s need to be repeated. For example, a 1 and a 6 totals 7, which can also be satisfied by a 2 and 5, or 3 and 4, etc.
How many ways you can rearrange the letters in the word french corner?
There is insufficient information for us to even begin to understand this question. Please edit the question to include more context or relevant information. You have not specified which word you want: french or corner.
What is the Uses of probability?
The uses of probability could be for the lottery, black jack or, your math homework.
Actuaries use probability factors to determine costs and risks. It is an entire science of its own and has a certification process. Insurance companies hire many actuaries to do probability calculations and create mortality tables.
What mumber is opposite 2 on the dice?
double it and that your answer!(4) like 3,6! and it you cant doulble it ( cus its not on the dice)then half it!
You must sample at 2 x the rate of the analog signal (2 x the analog signal frequency).
3c2+2c2+3c1 2c1
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7c2.
I have done it this way. 3C2 means that the both balls would be green 2C2 both would be red and 3C1 and 2C1 because both the balls can be red and green.
