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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
Primes are 2, 3, 5 and 7 which form 6 "prime pairs". There are 45 possible pairs in the box so the odds are 39 to 6 against ie 13/2, a probability of two-fifteenths or 13.3% or 0.13 recurring.
When is the median the most appropriate center for a distribution?
The median is the most appropriate center when the distribution is very skewed or if there are many outliers.
How do you find the standard deviation for the given probability distribution?
If the probability distribution function for the random variable X is f(x), then
first calculate E(X) = integral of x*f(x)dx over the whole real line.
Noxt calculate E(X2) = integral of x2*f(x)dx over the whole real line.
Then Variance(X) = E(X2) - [E(X)]2
and finally, SD(X) = sqrt[Variance(X)].
Can average deviation be negative?
No, average deviation cannot be negative.
Deviation is a representation of differences between numbers. A difference is always an absolute value, so the number cannot be negative (even though subtracting the deviation from an average may result in a a negative result).
How does 1 sigma represent 68.8 percent of the total area under a normal curve?
1 sigma does not represent 68.8 percent of anything.
The area under the standard normal curve, between -0.5 and +0.5, that i, the central 1 sigma, is equal to 0.68269 or 68.3%.
How many ways can 4 blocks be arranged?
As specified by the question, in infinitely many ways. Each block could be in four different places in the whole universe, with different orientations.
What is the probability of rolling an even number on 1 roll of a die?
There are 6 numbers on the die; 3 even. Therefore P(Even) = 3/6 or 1/2.
How does a z-score indicate how unusual a data value is?
It shows us by telling us how far away it is from the mean.
What season are rapes more likely to occur?
It has been confirmed that in the summer time more rapes happen. This is because during the summer kids are on their summer vacations so therefore means twice the rapes.
What is the chance of drawing a red ball from a bag containing 3 red and 2 white balls?
The probability is 1 if you draw three balls without replacement.
If only one draw, it is 3/5.
What is the sample space of tossing a coin 4 times?
The term 'sample space' can be somewhat arbitrary. In this case, it might be any of the following (or another) possibility:
If order of flips is significant:
HHHH
HHHT
HHTH
HHTT
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT
If order is not significant:
HHHH
HHHT
HHTT
HTTT
TTTT
If, say, only the number of either heads or tails is important:
4
3
2
1
Does an ogive best represent the shape of a distribution?
While a two-dimensional ogive or a cross-section of a three-dimensional ogive may represent the shape of a given distribution, they are only good for representing higher-likelihood (one- and two-sigma) outcomes because ogives do not have characteristic low-likelihood tails tails.
For very well managed processes (better than four sigma accuracy), a custom ogive may provide a very good approximation of resulting distribution.
It is 5C1*(1/10)1*(9/10)4 = 0.3281
This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.
Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,
For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:
However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.
A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint and
Sets that are not the same.
What is the number of marbles left in a 48-marble bag after some marbles have been givin away?
The number of marbles left in a 48 marble bag after some number N marbles have been given away is 48-N.
24
The first letter can be any of the 4. The second can be any of the remaining 3. The third, either remaining, and the last, the only remaining one. This means there are 4*3*2*1=24 different arrangements.
What are two ways mesopotamia and shang-china were similar and two ways they were different?
they are the same in politics and social structure, but they are different in politics
4:6 which equals 2:3 and 1:1.5
or in decimal 0.666667
