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BigorU [14]
3 years ago
12

F a gambler rolls two dice and gets the sum of 7, he wins $20. if he gets a sum of 4, he wins $40. the cost of playing is $14. w

hat is the expectation of this game?
Mathematics
1 answer:
DaniilM [7]3 years ago
3 0
The expectation of this game is that the house (casino) takes in roughly $3.83 every time someone plays, and after enough plays, they will typically always win. 

We can determine this case by looking at all of the possibilities and how much you can win or lose off of each. There are 36 total cases for what can happen when we roll the dice. Of those 36 cases, 9 of them produce positive winnings and 27 of them produce losses. 

To calculate the winnings, we need to look at what type they are. 6 of them will be 7's which earn the gambler $20. 3 of them would be 4's, which earns the gambler $40. 

6($20) + 3($40) 
$120 + $120
$240

Then we look at the losses. This is easier to calculate since every time the gambler loses, he losses exactly $14. There are 27 of these instances. 

27($14) 
$378

Now we can look at the average loss per game by subtracting the losses from the gains and finding the average. 

(Winnings - losses)/options
($240 - 378)/36
$3.83
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Sam and Sully are electricians. The graph represents the amount in dollars that Sam charges in terms of the number of hours he w
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The initial amount Sam charges is [$4 greater than] the initial amount Sully charges. Sam’s hourly rate is [$2 less than] Sully’s hourly rate.

A graph is attached for reference.

Step-by-step explanation:

Given is the graph that represents the amount in dollars that Sam charges in terms of the number of hours he works.

Where two points are (0,40) and (1,60).

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m=\frac{(y2-y1)}{(x2-x1)} \\m=\frac{(60-40)}{(1-0)} \\m=\frac{20}{1} \\m=20

Let us find the equation now,

y-y1 = m(x-x1)

Substituting (0,40) as (x1,y1) and slope m = 20

y-40=20(x-0)\\y-40 = 20x\\y= 20x+40

Here the 'y' intercept 40 represents the initial charge of Sam.

On comparing the equations of Sam and Sully we observe that Sam initial charge is 40  dollars.

And Sully's initial charge is 36  dollars.

Thus Sam's initial charge is $4 greater than Sully's.

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3 years ago
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