A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars

Answers

Answer 1

The expected net gain E(X) in the context of this problem is given as follows:

E(X) = -$0.5.

How to obtain the expected net gain?

The net gain for this problem is modeled for a discrete distribution, as there are only two possible outcomes, given as follows:

Winning $49.Losing $1.

The probability of winning is of 1% = 0.01, while the probability of losing is of 99% = 0.99, hence the distribution of gains for this problem is given as follows:

P(X = -1) = 0.99.P(X = 49) = 0.01.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

Hence the expected net gain for this game is calculated as follows:

E(X) = -1 x 0.99 + 49 x 0.01.

E(X) = -$0.5.

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Related Questions

You deposit $1000 in an account that pays 2% annual interest compounded quarterly. How much will you have
after 8 years?

Answers

Answer :
1,173.04

Explanation:
Use the compound interest formula which is P(1 + r/n)^(nt) and plug in your numbers:

1000(1+0.02/4)^(4•8)

Let n be the least positive integer for which 149^n-2^n is divisible by 3^3.5^5.7^7.$ Find the number of positive integer divisors of n.

Answers

Calculating the LCM of all these, one gets 2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}

Step-by-step explanation:

Note that for all n, 149^n-2^n is divisible by 149-2=147 by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3 is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.

Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.

Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}

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What is (-1)⁶?
O A. -i
O B.-1
O C. 1
O D. i

Answers

The answer would be : C) 1

help!!!! question is on the pic

Answers

Answer:

a. 110

Step-by-step explanation:

How do you get from 4 to 4/3?
4 times what gives us 4/3?

Answers

m = the unknown value

4m = four times that unknown value

4m = 4/3

m = (4/3)*(1/4)

m = 4/12

m = 1/3

Therefore, we multiply 4 with 1/3 to end up with 4/3.

Help me please, worth 25 points

Answers

Answer:

a=17.1

Step-by-step explanation:

sin20=a/50

50sin20=a

plug into calculator

The sum of four consecutive multiples of 7 is 406.

Work out the values of these four numbers.

Examples of four consecutive multiples of 7 are: 7, 14, 21, 28

Answers

The value of all four numbers will be 91, 98, 105, 112 respectively.

Let the first multiple be 7x

As the multiple of any number can be determined by simply multiplying the given number by the natural number or the counting numbers.

So, the value of the second multiple of 7 will be 7(x+1)

The value of third multiple of 7 will be = 7(x+2)

The value of fourth multiple of 7 will be = 7(x+3)

As all the multiple are consecutive so we have taken the multiplying factor as x, (x+1), (x+2) and (x+3)

From the data given in the question:

Sum = 7x+7x+7+7x+14+7x+21 = 406

=>28x+42=406

=>28x=364

=>x=(364/28)=13

So, the value of first multiple = 7x = (7*13) =91

So, the value of the second multiple of 7 will be 7(13+1)=98

The value of third multiple of 7 will be = 7(x+2)=7(13+2)=105

The value of fourth multiple of 7 will be = 7(x+3)=7(13+3)=112

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What is the area of the figure?

Answers

Answer:

151/6

Step-by-step explanation:

Adrian has $1 worth of nickels and dime. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Adrian has. Define the variables that you use to write the system.

Answers

Answer: We can use two variables, x and y, to represent the number of dimes and nickels Adrian has, respectively.

We know that Adrian has twice as many nickels as dimes, so we can write the equation:

y = 2x

We also know that the total value of the coins is $1, and since nickels and dimes have different values, we can write the equation:

0.05y + 0.1x = 1

So the system of equations is:

y = 2x

0.05y + 0.1x = 1

These equations can be solved simultaneously to find the number of nickels and dimes that Adrian has.

Step-by-step explanation:

Answer: X+ywwiww asksn q9ru3

Step-by-step explanation:

88-2

5. Step 4: Convert the number into decimal form rounded to the
nearest thousandth.

6.28=

O 6.284
O 6.280
O 6.283
O 6.282

Answers

Answer: 6.280

Step-by-step explanation:

Suppose y varies directly with x, and y = 6.5 when x = 1.3. What direct variation equation relates x and y ?

Select one:

a.
y = − 5x

b.
y = x / 5

c.
y = 5x

d.
y = 1.5x

Answers

Answer:

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 6.5 when x = 1.3

6.5 = 1.3k ( divide both sides by 1.3 )

5 = k

y = 5x ← equation of variation

7
What is the surface area of the figure below?
6 ft
3 ft
3 ft
A 12 ft?
B 36 ft?
© 54 ft?
D 90 ft?

Answers

The answer is 90 I think I multiplied 6*3 =18 *4 =72( for every rectangle )then 3*3 =9 for the square (2 squares ) 9*2=18

Coroline runs 3 1/2 miles in 22 1/4 minutes how many miles does she run per minute

Answers

Answer:

To determine the number of miles Coroline runs per minute, we need to first convert the distance she runs to a fraction of a mile and the time it takes her to run that distance to a fraction of an hour.

3 1/2 miles is equivalent to 3 + 1/2 = 3 + 1/(2*1) = 7/2 miles.

22 1/4 minutes is equivalent to 22 + 1/4 = 22 + 1/(4*1) = 23/4 minutes.

To convert the time to hours, we can divide the number of minutes by the number of minutes per hour. There are 60 minutes per hour, so we have:

23/4 minutes / (60 minutes/hour) = (23/4) / (60/4) = 23/60 hours

To determine the number of miles Coroline runs per minute, we can divide the distance she runs by the time it takes her to run that distance:

(7/2 miles) / (23/60 hours) = (7/2) / (23/60) = (760) / (223) = 420/46

Simplifying, we have:

420/46 = 9 1/23

Therefore, Coroline runs approximately 9 1/23 miles per minute.

Step-by-step explanation:

Answer:

she runs 0.078 miles per minute.

Step-by-step explanation:

How many possible three-card hands exist in a standard deck of 52 cards?

Answers

Answer:

we note that there 52 ways to choose the first card, 51 ways to choose the second card, and 50 ways to choose the third card, for a total of 52x51x50=132,600 ways.

Step-by-step explanation:

Answer:

4; 3 of spades, 3 of clubs, 3 of diamonds, and 3 of hearts

Step-by-step explanation:

In the figure shown, what is the value of x?
PLEASE HURRY JUST GIVE ME THE ANSWER THANK YOU

Answers

Answer: x= 23

Step-by-step explanation:

What are polynomials and its different types explain with examples?

Answers

Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.

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If PQR measures 75°, what is the measure of SQR?

22°
45°

Answers

The measure of the angle ∠PQS will be 53°. Then the correct option is C.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

If angle ∠PQR measures 75°. And angle ∠PQS measures 22°.

Angle ∠SQR and angle ∠PQS are the adjacent angles. Then we have

∠PQS + ∠SQR = ∠PQR

∠PQS + 22° = 75°

∠PQS = 53°

The measure of the angle ∠PQS will be 53°. Then the correct option is C.

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Complete question is attached below.

PLS HELP :[
The graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.

A graph shows Number of Pepperoni Rolls on x-axis and Price of Pepperoni Rolls on y-axis. The x-axis scale is shown from 0 to 24 at increments of 4, and the y-axis scale is shown from 0 to 160 at increments of 20. A straight line joins the ordered pairs 4, 20 and 8, 40 and 12, 60 and 16, 80 and 20, 100 and 24, 120.

Kaiser Roll Packet

Number of Kaiser Roll Packet

Price of Kaiser Roll Packet (dollars)

4

24

8

48

12

72

16

96

How many dollars more is the price of a Kaiser roll packet than the price of a pepperoni roll at Luis's store? (1 point)

a

$1

b

$4

c

$5

d

$6

Answers

Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

What is expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.

The price of a Kaiser roll packet = {C1} = (48 - 24)/(8 - 4) = 24/4 = 6

The price of a Kaiser roll = {C2} = (40 - 20)/(8 - 4) = 20/4 = 5

$6 - $5 = 1

Therefore, Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

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A guy wire attached to the top of a radio antenna

is bolted to the ground 48 m from the base of

the tower. If the wire makes an angle of 14°

with the ground. What is the length of the

guy wire? Round your answer to the nearest

hundredth of a meter.

1

Answers

The length of the guy wire is 48.87 m.

How to find the length?

To find the length of the guy wire, you can use the formula for the length of a side of a right triangle (the Pythagorean theorem): [tex]c = sqrt(a^2 + b^2)[/tex]. In this case, c is the length of the guy wire, a is the distance from the base of the tower to the point where the guy wire is attached to the ground (48 m), and b is the distance from the point where the guy wire is attached to the ground to the top of the antenna.

To find b, you can use the tangent function: [tex]tan(14°) = b / 48.[/tex]

Solving for b gives b = 6.78 m

Then, length of wire can be calculated as

[tex]c = sqrt(48^2 + 6.78^2)[/tex]

[tex]c = 48.87 m (approx)[/tex]

Rounding it to the nearest hundredth of a meter, the length of the guy wire is 48.87 m.

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Before sending track and field athletes to the Olympics, the U. S. Holds a qualifying meet. The upper box plot shows the top 12 men's long jumpers at the U. S. Qualifying meet. The lower box plot shows the distances (in meters) achieved in the men's long jump at the 2012 Olympic games. Which pieces of information can be gathered from these box plots?

Answers

We require median, interquartile range, outliers, minimum and maximum value.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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We require median, interquartile range, outliers, and minimum and maximum values.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.