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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
Prior probability is the probability that is assessed before reference is made to relevant observations.
For complex events, it is possible to calculate the probability of events, but often extremely difficult. In the given example, for an "average" person (that would need some definition to start with) you would need to know the probability of them scoring a basket without the blindfold - this can be found by observing a number of "average" people attempting a number of baskets and seeing how many are successful (the greater the number of observations, the better the accuracy of the [estimation of the] probability. Also, the effect of blindfolding them needs to be found - this is not so easy, but some measure could possibly be made - and then combining this effect and the probability found some estimation of the probability of the required event can be calculated.
Someone has analysed tennis scoring and given the probability of one of the players winning a point (which can be estimated fairly accurately through past observation) has calculated the probability of them winning the match; however, each match (and even a game within a match) can be affected by further factors (eg one player suffering a small injury) which modify the probability of winning a point, but a calculated probability can still be made.
Are m and f mutually exclusive?
If by this you mean male and female then no. Although rare individuals with ambiguous characteristics do occur naturally in human and animal populations. Please see the wikipedia article entitled 'intersex' for more information.
What is the standard normal deviation?
The standard deviation of a normal deviation is the square root of the mean, also the square root of the variance.
CANOY a family last name & not canopy is what I am wanting to know.
Find the probability of rolling a 10 with two dice?
Assuming that the random variable is the sum of the two numbers rolled, the answer is 3/36 or 1/12.
How do you deal with cicle theorems?
A line joining the centre of a circle to any of the points on the circle is known as a radius.
The circumference of a circle is the length of the circle. The circumference of a circle = 2 × π × the radius.
The red line in the second diagram is called a chord. It divides the circle into a major segment and a minor segment.
TheoremsAngles Subtended on the Same ArcAngles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.
Angle in a Semi-CircleAngles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle.
ProofWe can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches.
We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles.
But all of these angles together must add up to 180°, since they are the angles of the original big triangle.
Therefore x + y + x + y = 180, in other words 2(x + y) = 180.
and so x + y = 90. But x + y is the size of the angle we wanted to find.
TangentsA tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent.
Also, if two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same.
Angle at the CentreThe angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.
ProofYou might have to be able to prove this fact:
OA = OX since both of these are equal to the radius of the circle. The triangle AOX is therefore isosceles and so ∠OXA = a
Similarly, ∠OXB = b
Since the angles in a triangle add up to 180, we know that ∠XOA = 180 - 2a
Similarly, ∠BOX = 180 - 2b
Since the angles around a point add up to 360, we have that ∠AOB = 360 - ∠XOA - ∠BOX
= 360 - (180 - 2a) - (180 - 2b)
= 2a + 2b = 2(a + b) = 2 ∠AXB
Alternate Segment TheoremThis diagram shows the alternate segment theorem. In short, the red angles are equal to each other and the green angles are equal to each other.
ProofYou may have to be able to prove the alternate segment theorem:
We use facts about related angles:
A tangent makes an angle of 90 degrees with the radius of a circle, so we know that ∠OAC + x = 90.
The angle in a semi-circle is 90, so ∠BCA = 90.
The angles in a triangle add up to 180, so ∠BCA + ∠OAC + y = 180
Therefore 90 + ∠OAC + y = 180 and so ∠OAC + y = 90
But OAC + x = 90, so ∠OAC + x = ∠OAC + y
Hence x = y
Cyclic QuadrilateralsA cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees. Area of Sector and Arc LengthIf the radius of the circle is r,
Area of sector = πr2 × A/360
Arc length = 2πr × A/360
In other words, area of sector = area of circle × A/360
arc length = circumference of circle × A/360
The number of combinations for trumpet players * the combinations for guitarists * the combinations for saxophonists
= (4!/(2!(4-2)!))* (12!/(5!(12-5)!))* (7!/(3!(7-3)!))
= (4!/(2!*2!))* (12!/(5!*7!))* (7!/(3!*4!))
= (6)* ((12*11*10*9*8)/(5*4*3*2))* (7*6*5/(3*2))
= 6*792*35
= 166320
What is the probability of three?
The answer will depend on what the experiment is: rolling a die, spinning a spinner, the number of times someone will lose before they win (or the converse), the number of rooms in a house, or whatever. Since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
What are examples of mathematical probabilities?
Here are some:
- If you have a bag of 10 marbles, 6 of which are red, the chance of taking out a red one at random is 3/5
- If you roll a dice, the chance of getting an even number is 1/2
- If you take the top card of a shuffled deck the chance of it being a diamond is 1/4. The chance of it being a king is 1/13
Does variance provide more information than standard deviation?
No. Because standard deviation is simply the square root of the variance, their information content is exactly the same.
What is the probability that the division of 1099 is a multiple of 1096?
If there is an integer by which 1099 can be divided that will result in a multiple of 1096, it would have to be 1/1096, resulting in 1204504. I think this is the only one that completely fills the requirements. Dividing 1099 by something that gets you a multiple of 1096 requires dividing by the reciprocal of the factor.
If one occurrence is true, probability is 100%.
What are the measurements that fall beyond three standard deviations from the mean?
They are observations with a low likelihood of occurrence. They may be called outliers but there is no agreed definition for outliers.
What is the calulated value of the standard deviation of returns for -22.0 -2.0 20.0 35.0 and 50.0?
It is 28.73
What is the probabiltiy of landing on a number with 3 factors on a spinner with 8 possible outcomes?
The answer will depend on what the 8 numbers on the spinner are!
Total number of woman over total number of people
So for this problem it's 23/41
The mathematical probability of getting heads is 0.5. 70 heads out of 100 tosses represents a probability of 0.7 which is 40% larger.
1.6
If you go back 34 generations you have 17 billion direct ancestors. How is this possible?
It is not possible. There have never been half that number of people alive at any one time.
This calculation is a crude demonstration, among other things, that everyone is related, however distantly, to everyone else.
