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2 years ago

Which of the following is an example of a random event?

2 answers:

7 0

A concept of an event is an extremely important in the Theory of Probabilities. Actually, it's one of the fundamental concepts, like a point in Geometry or equation in Algebra.
First of all, we consider a random experiment - any physical or mental act that has certain number of outcomes. For example, we count money in our wallet or predict tomorrow's stock market index value. In both and many other cases the random experiment results in certain outcomes (the exact amount of money, the exact stock market index value etc.) These individual outcomes are called elementary events and all such elementary events associated with a particular random experiment together form a sample space of this experiment.
More rigorously, the sample space of any random experiment is a SET and all individual elementary events (that is, the individual results of this experiment) are ELEMENTS of this set.
Now we can consider not only an individual elementary event, like exact amount of money in a wallet, but a combination of such elementary events. For instance, we can consider the result of our money counting experiment to be less than $5. This is a combined event that consists of elementary events $0, $1, $2, $3 and $4. This and other combinations of elementary events is called a random event.
Using our SET terminology, a random event is a SUBSET of a SET of all elementary events (in other words, a SUBSET of a sample space). Any such SUBSET is called a random event.
In Theory of Probabilities there is a concept of probability associated with each elementary event. If the number of elementary events is finite or countable, this probability is just a non-negative number and the sum (even infinite sum in case of countable number of elementary events) equals to 1.
The probability associated with any random event is a sum of probabilities of all elementary events that comprise it.

Lady_Fox [76]2 years ago

6 0

Random events are events that do not have an exact outcome. The set of possible outcomes for a random event is always more than one item or amount. For example we can think about the total amount of our money counting experiment to be less than $5. This is a combined event that have elementary events $0, $1, $2, $3 and $4. This is called a random event.

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brilliants [131]

Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

4 0

3 years ago

Help me pls I,need it very much

Sunny_sXe [5.5K]

A straight line is 180 degrees. As a result, 180-35=x, or x=145

3 0

3 years ago

John jogged 4 1/2 miles. Susan jogged 1/4 of the miles that John jogged. How many miles did Susan jog?

Kobotan [32]

Answer:

Susan jogged 1 1/8 miles

Step-by-step explanation:

4 1/2= 18/4. 18/4 ÷ 1/4= 1.125= 1 1/8

6 0

3 years ago

Which operation should you perform last in the expression 12 × 42?

GrogVix [38]

Answer:

The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.

Step-by-step explanation:

6 0

1 year ago

Read 2 more answers

What are three even numbers that are less than 10 and have a sum of 18. PLZ HELP MEH

Maksim231197 [3]

8, 6, and 4.
Eight plus six equals: 14
Then add four, and your get eighteen
~Hope this helped :)

3 0

3 years ago

Read 2 more answers