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frez [133]
1 year ago
14

In a state's Pick 3 lottery game, you pay $1.35 to select a sequence of three digits (from 0 to 9), such as 366. If you select t

he same sequence of three digits that are drawn, you win and collect $477.75. Find the expected value.
Mathematics
1 answer:
tia_tia [17]1 year ago
5 0

Let us first review what we are given in the problem:

the game costs $1.35

3 digits are to be selected from 0 to 9

repetition is allowed (based on the given example)

a winning sequence earns $477.75

a. How many different selections are possible?

There are three slots and each slot has 10 digits to choose from. So there are 10 x 10 x 10 = 1,000 possible selections (from 000 up to 999)

b. What is the probability of winning?

The probablity of winning is equal to the number of ways you can win, divided by the total number of possible selections. Since there is ony one sequence that will win, then the answer is 1/1,000 or 0.001.

c. If you win, what is your net profit?

If you win, then your profit is equal to $477.75 minus the cost of joining the game, which is $1.35. So your profit is $476.40.

Note that if you do not win, then you lose the $1.35 you paid for joining the game.

d. Find the expected value.

The expected value is equal to the summation of all the possible outcomes (profits or losses) multiplied by their corresponding probabilities. So we calculate it as follows:

\begin{gathered} E(x)=\sum_^xP(x) \\  \\ E(x)=476.40(0.001)+(-1.35)(1-0.001) \\ E(x)=476.40(0.001)+(-1.35)(0.999) \\ E(x)=-0.87225 \end{gathered}

The expected value is -0.87 or a loss of $0.87.

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lesya692 [45]

This is an example of a piecewise defined function. It means that the function has not a unique formula to represent it, but it depends on "where" you want to compute it.

So, if you choose any input x, you have two alternative:

  • If x \neq 3 (i.e., if you've chosen any input that is not 3), the output will be the opposite of the input you've chosen (y=-x)
  • If x=3, the ouput will be -1.

So, let's forget about x=3 for a moment. For any input x you choose, the answer is -x. The graph of this function is the bisector of the second and fourth quadrant.

Now remember that there is our special case: you have to "carve a hole" in our line, at x=3, and assing to this point the value -1, instead of what we would expect, i.e. -3.

So, the graph of this function is the line y=-x, except for one point (x=3), where we reassign the value to be -1.

5 0
3 years ago
My digits are consecutive numbers.
Alchen [17]

Answer:

456 is the number you are looking for.

Step-by-step explanation:

Consecutive numbers are numbers which continuously follow each other in the order from smallest to largest.

Have a nice day!

6 0
2 years ago
52.85-9.09 rounded to the nearest one
Mkey [24]
53, and 9. Are the answers.
8 0
3 years ago
An individual needs a daily supplement of at least 420 units of vitamin C and 170 units of vitamin E and agrees to obtain this s
Ierofanga [76]

Answer:

To obtain equivalent amount from both foods we can eat 10 ounces of Food I and 5 Ounces of food II

To obtain minimum cholesterol, the individual should eat only 21 ounces of food II and zero ounce of food for the daily supplement of the individual

Step-by-step explanation:

Food I contains 32×C + 10×E per ounce

Food II contains 20×C + 14×E  

Here we have X × (Food I) + Y × (Food II) = 420 C + 170 E

32·X + 20·Y = 420 C

10·X + 14·Y = 170 E

Therefore

X = 10 and Y = 5

To minimize the cholesterol, we can increase amount of Food II to get

21 ounces of food II gives

420 units of vitamin E and 294 units of vitamin E with 273 units of cholesterol.

 

                     

3 0
3 years ago
What is the answer of 12x - 6 = 54
Bogdan [553]

Answer:

x = 5

Step-by-step explanation:

12x - 6 + 6 = 54 + 6

12x = 60

12/12 = 60/12

X = 5

7 0
1 year ago
Read 2 more answers
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