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dmitriy555 [2]
2 years ago
14

Suppose someone gives you 8 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win ​

$ if you succeed and you lose ​$ if you fail. What is the expected value of this game to​ you? Should you expect to win or lose the expected value in the first​ game? What can you expect if you play ​times? Explain.
Mathematics
1 answer:
krek1111 [17]2 years ago
6 0

Complete question :

Suppose someone gives you 8 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $8 if you succeed and you lose $2 if you fail. What is the expected value of this game to​ you? What can you expect if you play 100 times.

Answer:

$0.5 ; win $50 with 100 rolls

Step-by-step explanation:

From a roll of two fair dice; probability of obtaining an even number :

Even numbers = (2, 4, 6) = 3

P = 3 /6 = 1 /2

For 2 fair dice ; probability of rolling two even numbers : independent event.

1/2 * 1/2 = 1/4

Hence, p(success) = 1/4 ; P(failure) = 1 - 1/4 = 3/4

Probability table

Winning = $8 or loss = - $2

X : ____ 8 ______ - 2

P(x) __ 1/4 ______ 3/4

Expected value : E(x) = ΣX*P(x)

E(x) = (8 * 1/4) + (-2 * 3/4)

E(x) = 2 - 1.5

E(x) = $0.5

Since expected value is positive, the expect to win

If played 100 times;

Expected value = 100 * $0.5 = $50

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Using it's concept, it is found that the domain for the expressions is, respectively, given by:

x \neq 0, x \neq 0, (-\infty, \infty), (-\infty, \infty), x \neq 2

<h3>What is the domain of a function?</h3>

It is the <u>set that contains all possible input values</u>.

In a fraction, the denominator cannot be zero, hence:

  • The domain of the first two expressions is of x \neq 0.
  • The domain of the last expression is of x \neq 2.

The third expression can be simplified, as:

(x + 5)/(x + 5) = 1.

The same is true for the fourth, as:

x²/x = 1.

Neither has any restriction, hence their domain is all real numbers, represented by (-\infty, \infty).

More can be learned about the domain of a function at brainly.com/question/25897115

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2 years ago
A word problem for the expression 5+(-2) The sum will be three i just need a word problem
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Mikey had 5 cookies. His friend took 2 with him when he left. How many cookies does Mikey have left?

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3 years ago
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Ok. so, you have a fraction. lets say it is, 5/20. and the other, is. 2/5. flip the first one, and multiply. so your answer would be, 25/40. hope this helps.
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3 years ago
A stadium has a a central rectangular area 125m long by 80m wide.there are two semi circular ends.a running track goes all the w
Fudgin [204]

a)The total inside length of the curved ends of the track will be 25.13 meters

b)The total distance around the inside of the track will be 275.13 meters

c)The area inside the track is 10050 square meters.

<h3>What is an area?</h3>

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that:-

A stadium has a central rectangular area 125m long by 80m wide. there are two semi-circular ends. a running track goes all the way around.

a) what is the total inside length of the curved ends of the track?

The length of the curved track means it is a perimeter of the circle so the radius of the semicircle will be 4 meters.

So the length will be = π r + πr = 2 πr

                                  = 2 x π x 4 = 25.13

b) what is the total distance around the inside of the track?

The total distance of the track will be the sum of the length of the two semicircles and the longer side of the rectangle.

Total length = 125 + 125 + 25.13

                     = 275.13 meters

c) what is the area inside of the track?

The area will be equal to the area of the two semicircular tracks and the rectangular track.

Total Area = Area of semicircle + Area of semicircle + Area of rectangle

                  = ( π/2 ) r² + (π/2) r² + ( L x W )

                  =  π  r² + (  L x W)

                  = π ( 4 )² + ( 125 x 8 )

                  = 10050.26 square meters.

Therefore the total inside length of the curved ends of the track will be 25.13 meters. The total distance around the inside of the track will be 275.13 meters. The area inside the track is 10050 square meters.

To know more about an area follow

brainly.com/question/25292087

#SPJ1

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2 years ago
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