Gianna is converting a 12-foot-by-15-foot room in her

Your friend asks if you would like to play a game of chance that uses a deck of cards and costs $1 to play. They say that if you

gtnhenbr [62]

Answer:

Expected value = 40/26 = 1.54 approximately

The player expects to win on average about $1.54 per game.

The positive expected value means it's a good idea to play the game.

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Further Explanation:

Let's label the three scenarios like so

scenario A: selecting a black card
scenario B: selecting a red card that is less than 5
scenario C: selecting anything that doesn't fit with the previous scenarios

The probability of scenario A happening is 1/2 because half the cards are black. Or you can notice that there are 26 black cards (13 spade + 13 club) out of 52 total, so 26/52 = 1/2. The net pay off for scenario A is 2-1 = 1 dollar because we have to account for the price to play the game.

-----------------

Now onto scenario B.

The cards that are less than five are: {A, 2, 3, 4}. I'm considering aces to be smaller than 2. There are 2 sets of these values to account for the two red suits (hearts and diamonds), meaning there are 4*2 = 8 such cards out of 52 total. Then note that 8/52 = 2/13. The probability of winning $10 is 2/13. Though the net pay off here is 10-1 = 9 dollars to account for the cost to play the game.

So far the fractions we found for scenarios A and B were: 1/2 and 2/13

Let's get each fraction to the same denominator

1/2 = 13/26
2/13 = 4/26

Then add them up

13/26 + 4/26 = 17/26

Next, subtract the value from 1

1 - (17/26) = 26/26 - 17/26 = 9/26

The fraction 9/26 represents the chances of getting anything other than scenario A or scenario B. The net pay off here is -1 to indicate you lose one dollar.

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Here's a table to organize everything so far

$\begin{array}{|c|c|c|}\cline{1-3}\text{Scenario} & \text{Probability} & \text{Net Payoff}\\ \cline{1-3}\text{A} & 1/2 & 1\\ \cline{1-3}\text{B} & 2/13 & 9\\ \cline{1-3}\text{C} & 9/26 & -1\\ \cline{1-3}\end{array}$

What we do from here is multiply each probability with the corresponding net payoff. I'll write the results in the fourth column as shown below

$\begin{array}{|c|c|c|c|}\cline{1-4}\text{Scenario} & \text{Probability} & \text{Net Payoff} & \text{Probability * Payoff}\\ \cline{1-4}\text{A} & 1/2 & 1 & 1/2\\ \cline{1-4}\text{B} & 2/13 & 9 & 18/13\\ \cline{1-4}\text{C} & 9/26 & -1 & -9/26\\ \cline{1-4}\end{array}$

Then we add up the results of that fourth column to compute the expected value.

(1/2) + (18/13) + (-9/26)

13/26 + 36/26 - 9/26

(13+36-9)/26

40/26

1.538 approximately

This value rounds to 1.54

The expected value for the player is 1.54 which means they expect to win, on average, about $1.54 per game.

Therefore, this game is tilted in favor of the player and it's a good decision to play the game.

If the expected value was negative, then the player would lose money on average and the game wouldn't be a good idea to play (though the card dealer would be happy).

Having an expected value of 0 would indicate a mathematically fair game, as no side gains money nor do they lose money on average.

7 0

2 years ago

Whoever answers this can you please like show how you did it Idk how to do it

shusha [124]

Answer:

a) 2500 L b) 2250 L c) 98000 L d) 14.5 kg of rice, .725 kg of beef, 48.3 repeating kg of wheat.

Step-by-step explanation:

Ok so, this question looks intimidating but I promise it's not that bad.

a) They're asking how much water (L - meaning liters) would be needed for 25 baths.

To find this, they already give you how much water is needed for 1 bath. (100) Since this is the amount for 1 bath, we can find how much water is needed for 25 baths by multiplying 100 by 25. Your answer should be 2500 L of water.

b) This is the same thing again, but with wheat. They give us the information for how much wheat is used for 1 kg of wheat, which is 600 L. The question asks how much water would be needed to produce 3.75 kg of wheat, so we multiply 600 by 3.75 which equals 2250 L.

c) This is also the same thing but this time for beef. So we multiply 40000 by 2.45 which gives us 98000 L

d) To find this, we must divide 29,000 by the amount of water needed for 1 of each item, so we can find how much we would multiply the amount needed for 1 of each item in the first place (which is the amount of rice, beef, wheat)

So, 29,000/2000 = 14.5 kg of rice

29,000/40000 = .725 kg of beef

29,000/600 = 48.3 repeating kg of wheat.

3 0

3 years ago

Whose responsibility is it to call out the government and point out flaws

Jlenok [28]

Adults, 18 and older

7 0

2 years ago

I need help with number 4

Nadusha1986 [10]

$\bf \begin{cases}
\quad3x+2y=-9\\
-10x+5y=-5
\end{cases}$

so hmm the idea behind the elimination, is to make the value atop or below, of either variable, the same but with a negative sign

so hmmm say... we'll eliminate "y"

so... let's see, we have 2y and 5y, both positive
what do we multiply 2y to get a negative -5y, that way, -5y +5y = 0 and poof it goes

well let's see, let's try "k" $\bf 2yk=-5y\implies k=-\cfrac{5y}{2y}\implies k=-\cfrac{5}{2}$

so.. if we multiply 2y by -5/2, we'll end up with -5y

well, let's multiply that first equation then by -5/2

$\bf \begin{array}{rllll}
3x+2y=-9&\qquad\times -\frac{5}{2}\implies &-\frac{15}{2}x-5y=\frac{45}{2}\\\\
-10x+5y=-5&\implies &-10x+5y=-5\\
&&---------\\
&&\frac{-35}{2}x+0\quad=\frac{35}{2}
\end{array}\\\\
-----------------------------\\\\
\cfrac{-35}{2}x=\cfrac{-35}{2}\implies \cfrac{-35x}{2}=\cfrac{-35}{2}\implies x=\cfrac{2}{-35}\cdot \cfrac{-35}{2}
\\\\\\
\boxed{x=1}$

so.. now we know x = 1.... so let's plug that in say hmmm 2nd equation

$\bf -10(1)+5y=-5\implies -10+5y=-5\implies 5y=5\implies\boxed{ y=1}$

3 0

3 years ago

I need help solving these question I’ll give brainleiest

denis-greek [22]

4. -5+8
5. 14x
6. 3+6x
7. -1x +-2
8. X
9. 15x+5

4 0

2 years ago

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