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2 years ago

Which inequality statement best describes the probability of event (P) ?

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

6 0

Answer:

$0\le P\le 1$

Step-by-step explanation:

The probability of an event is a number describing the chance that the event will happen.

Definition: The probability of an evant is

$P=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}$

1. An event that is certain to happen (Number of favorable outcomes = Number of all possible outcomes) has a probability of 1.

2. An event that cannot possibly happen (Number of favorable outcomes = 0) has a probability of 0.

3. If there is a chance that an event will happen, then its probability is between 0 and 1.

Thus,

$0\le P\le 1$

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A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is $\binom{5}{1}\cdot \binom{5}{1}$ . So, we define the following probabilities.

Probability of winning: $\frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}$

Probability of losing $\frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}$

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing = $1.10\cdot \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}$

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing = $1.10^2\cdot \frac{4}{9}+\frac{5}{9}=\frac{82}{75}$

We will use the following formula

$Var(X) = E(X^2)-E(X)^2$

Thus

Var(X) = $\frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}$

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2 years ago

The equation y = negative StartFraction 1 Over 20 EndFraction x + 10 represents the gallons of gasoline that remain in Michelle’

andrey2020 [161]

The graph must look like this (see attached):

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2 years ago

Read 2 more answers

Which of the following best describes the slope of the line below?

Aleonysh [2.5K]

Answer:

it is undefined

Step-by-step explanation:

it is undefined because the vertical line touches the same x coordinate in the whole thing.

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2 years ago

Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6. What is t

Pani-rosa [81]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

Given: Two distinct number cubes, one red and one blue, are rolled together

To find: probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

Solution:

If two dices are rolled together, possible outcomes are as follows:

(1,1) (1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

So, total number of outcomes = 36

In order to find probability that the outcome of the roll is an even sum or a sum that is a multiple of 3, favourable outcomes are

(1,1) (1,2)(1,3)(1,5)

(2,1)(2,2)(2,4)(2,6)

(3,1)(3,3)(3,5)(3,6)

(4,2)(4,4)(4,5)(4,6)

(5,1)(5,3)(5,4)(5,5)

(6,2)(6,3)(6,4)(6,6)

Number of favourable outcomes = 24

Probability that the outcome of the roll is an even sum or a sum that is a multiple of 3 = Number of favourable outcomes/Total Number of outcomes = $\frac{24}{36} =\frac{2}{3}$

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2 years ago

Two parabolas have the same focus, namely the point $(3,-28).$ Their directrices are the $x$-axis and the $y$-axis, respectively

jeyben [28]

Answer:

the slope of the common cord is: $-1$

Step-by-step explanation:

Given the focus (a,b) = (3,-28)

for a parabola with directrix at x-axis the equation will be

$\left(x-a\right)^{2}+\left(y-b\right)^{2}=y^{2}$

$\left(x-a\right)^{2}+\left(y-b\right)^{2}-y^{2}=0$

for a parabola with directrix at y-axis the equation will be

$\left(x-a\right)^{2}+\left(y-b\right)^{2}=x^{2}$

$\left(x-a\right)^{2}+\left(y-b\right)^{2}-x^{2}=0$

The common chord is the line between two points where the two parabolas intersect. For intersection, we can equate the two parabolas!

In other words, at the point of intersection of these two parabolas the values of the two parabolas will be the same.

$\left(x-a\right)^{2}+\left(y-b\right)^{2}-y^{2}=\left(x-a\right)^{2}+\left(y-b\right)^{2}-x^{2}$

$\left(x-3\right)^{2}+\left(y+28\right)^{2}-y^{2}=\left(x-3\right)^{2}+\left(y+28\right)^{2}-x^{2}$

we can now simplify the equation. (we can see that (x-3) and (y+28) both cancel out by -(x-3) and -(y+28))

$-y^{2}=-x^{2}$

$y=\sqrt{x^{2}}$

$y=\pm x$

this the equation of the common cord. but we need to select whether its

$y=+ x$ or $y=-x$ .

This can be found by realizing that the focus lies on the 4th quadrant of the xy-plane! And the equation $y=-x$ also generates a line that exists in the 2nd and 4th quadrant.

Hence the slope of the common cord is the slope of the line $y=-x$

that is : $-1$

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2 years ago