Probability Example

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. what is the probability that the ball is red? 
By using the basics of probability, Total numbers of balls are 3 + 5 = 8, and Number of red balls are 3, Therefore,
Probability (Red Ball) = 3/8

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Theoritical Probability basic

Theoretical Probability of an event

If there are n events associated with a random experiment and m of them are the favorable to the event E, then the Probability of the event E is denoted by P(E) is defined by


    P(E) = numbers of outcomes favorable to E/number ber of all possible Outcomes = m/n

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Solving Trigonometric Equations - General Solutions

Solving Trigonometric Equations - General Solutions

An Equation involving trigonometric functions is called a trigonometric equation. For example,
     sinx = 0.50, tan A = 0.75
In this section we just find out the general solution to these given equations.

Let's check, tan A = 0.75, Using the inverse trigonometric function of tangent i.e. tan ^-1 0.75 =38 degree (approx).
We also know that the tangent function has a period of pi = 180 degree radian and its repeats every 180. in this situation there are many possible answers of this trigonometric functions.
    A = 38 + 180 n
where n = 1,2,3,... and you find the most general solution of trigonometric equations.

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General Triangles solution using laws of sine and cosine formula

General Triangles :  Solutions
For a general triangle, which may or may not have a right angle, we will again need three pieces of information. The four cases are:

1.  One side and two angles
2. Two sides and one opposite angle
3. Two sides and the angle between them
4. Three sides are given

Note that if we were given all three angles we could not determine the sides uniquely; by similarity an infinite number of triangles have the same angles.

To solve a general triangle in all four of the above cases. Though the methods described will work for right triangles, they are mostly used to solve oblique triangles, that is, triangles which do not have a right angle.

There are two types of oblique triangles: an acute triangle has all acute angles, and an obtuse triangle has one obtuse angle.

Also Understand the concept of laws of sines and laws of cosines formulas

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Parallel and Perpendicular Lines Online Algebra Free Help

Parallel and Perpendicular Lines

Two lines with the same slope are said to be a parallel lines. When we plot a graph of parallel lines then they will never intersect to each other. Line AB and Line CD are Parallel lines and it is denoted by AB||CD.

The equation of the straight lines are y = m1x + c and y = m2x + c are parallel  if the slopes of both lines are equal i.e.  m1 = m2 and the lines are perpendicular lines if m1m2 = -1.

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Free math education online tutorials

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