Instruction

1

The classical formula of probability (Laplace's equation) is:

P(A) = M/N, where

P(A) is the probability of a

M is the number of elementary events favorable to event A

N is the number of all elementary events.Two simplest examples. In a situation of flipping a coin when you need to calculate the probability of getting tails (event A), is conducive to the event And it itself. If you want to calculate the probability of even faces with the dice favourable elementary events will have three (as can fall three even numbers). Accordingly, the probability of an event A will be 0.5 in the first and second cases.

P(A) = M/N, where

P(A) is the probability of a

M is the number of elementary events favorable to event A

N is the number of all elementary events.Two simplest examples. In a situation of flipping a coin when you need to calculate the probability of getting tails (event A), is conducive to the event And it itself. If you want to calculate the probability of even faces with the dice favourable elementary events will have three (as can fall three even numbers). Accordingly, the probability of an event A will be 0.5 in the first and second cases.

2

A few words about the opportunities. In probability theory an event that will happen necessarily, is called "authentic" (probability equal to one). The opposite of reliable is "impossible" event (probability is zero). An event that may happen or may not happen, is called "random" (probability of random events 0

3

There is another definition of probability (more precisely, the geometric interpretation of probability):P(A) = Q/S, where

S – the area of the shape that a randomly thrown point

Q – part of the area of a shape S, which misses the point.

P(A) is the probability that a randomly thrown point to the area Q.

S – the area of the shape that a randomly thrown point

Q – part of the area of a shape S, which misses the point.

P(A) is the probability that a randomly thrown point to the area Q.

4

A classical problem in geometric probability: suppose that we are given a square which is inscribed in a circle. In the square drop out point; the probability that it falls in a circle is equal to the ratio of areas of circle and square (the solution of the problem, see the picture).

# Advice 2: How to calculate the accuracy

To compare two samples drawn from the same underlying population, or two different States of one and the same set method is used student. It can be used to calculate the significance of differences, that is, to know the trustworthiness of the conducted measurements.

Instruction

1

In order to choose the right formula of reliability, determine the value of groups of samples. If the number of measurements is greater than 30, such a group would be considered large. Thus, there are three options: both groups are small, the two large groups, one small group, the second – biggest.

2

In addition, you will need to know, dependent on whether the measurement of the first group with the second measurement. If each i-th variant of the first group opposed to the i-th embodiment of the second group, they are pairwise dependent. If the options within the group can be interchanged, such groups are called groups with pairwise-independent variants.

3

For comparison of groups with pairwise-independent options (at least one of them must be big), use the formula presented in the figure. Using the formula you can find the student's criterion, it determines a confidence probability of the differences between the two groups.

4

To determine the student's t-test for small size groups with pairwise-independent options, use another formula, it is represented in the second picture. The number of degrees of freedom is calculated in the same way as in the first case: fold the volume of the two samples and subtract the number 2.

5

To compare two small groups with pairwise-dependent results using two formulas of your choice. The number of degrees of freedom is calculated differently according to the formula k=2*(n-1).

6

Next, specify confidence probability according to the table t-student's t test. In this case, note that the sample was reliable, confidence probability must be at least 95%. That is, find the first column value of the number of degrees of freedom, and the first line is a calculated student's criterion and rate, more or less, the resulting probability of 95%.

7

For example, you received t=2,3; k=73. On the table to determine a confidence probability, it is more than 95%, therefore, the differences of the samples is accurate. Another example: t=1,4; k=70. According to the table below to the minimum value for 95% confidence, k=70, t must be equal to at least of 1.98. You have the same it is less - only 1.4, so the difference of the samples unreliable.

# Advice 3: How to calculate the probability of the event

Under

**the probabilityu**is generally understood numerically expressed measure of the ability of the onset of an**event**. In practical application, this measure acts as a ratio of the number of observations in which a particular event occurred, to the total number of observations in a random experiment.You will need

- paper;
- pencil;
- calculator.

Instruction

1

For example, the calculation of the probability let us consider the simplest situation in which you want to define the amount of confidence that a standard set of cards containing 36 elements, you randomly pull any ACE. In this case, the probability P(a) will equal a fraction, the numerator of which is the number of favorable outcomes X and the denominator is the total number possible in the experiment of event Y.

2

Determine the number of favorable outcomes. In this example it will be 4 since in a standard deck of cards has exactly this number of aces of different suits.

3

Count the total number of possible events. Each card in the set has its own unique advantage, so for a standard deck of 36 possible options of a single choice. Of course, prior experience should take the condition under which all the cards are in the deck and are not repeated.

4

Select the likelihood that you removed from the deck one card is any ACE. To do this, use the formula: P(a) = X/Y = 4/36 = 1/9. In other words, the probability that the taking of a set of one card, you will receive the ACE, a relatively small and equal to about 0,11.

5

Change the conditions of the experiment. Let's say that you are going to calculate the probability of occurrence of

**events**, when taken at random card from the same set will be the ACE of spades. The number of favorable outcomes corresponding to the condition of the experiment, changed to become equal to 1, since the set only one card of the specified advantages.6

Put new data in the above formula P(a). So, P(a) = 1/36. In other words, the probability of a positive outcome of the second experiment decreased four times and made up approximately 0,027.

7

When calculating the probability of occurrence of

**events**in the experiment consider that you need to count all possible outcomes, reflected in the denominator. Otherwise, the result will present a distorted picture of the probability.