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zysi [14]
3 years ago
12

A casino offers a game in which a player places a $3 bet on a 3 coming up on one roll of a six-sided die. If a 3 is rolled, the

player keeps their $3 and is paid $12 by the house. If a number other than 3 is rolled, the house keeps the player's $3. What is the expected value of this game to the player?
Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
3 0

Answer:

Expected Value = -1$

Step-by-step explanation:

Expected Value: So, expected value is the very important concept of probability, from insurance to governments, from casinos to lotteries the concept of expected value is used. It is basically the expected gain or loss when you perform the task repeatedly.

So here’s the question statement:

Bet = 3$  

Bet is on: Number 3 of a 6 faced dice.

Total numbers on dice = 6 = Total number of outcomes

Bet is on how many numbers = 1 = Number of Favorable outcomes.

If you win: you will get:     12$ = 3$ (Bet amount) + 9$ (outcome)

Outcome of winning = 9$

Probability of winning = Favorable outcome divided by Total number of outcomes = 1/6 = 0.16666..

If you lose you will lose:   3$ (Bet amount)

Outcome of losing = -3$ ( - “minus” represents losing)

Probability of losing = Favorable outcome divided by Total number of outcomes = 5/6 = 0.8333…

So, expected value is calculated when you play this game repeatedly right?

Formula to calculate Expected Value:

Expected Value = (Outcome of Winning) x (Probability of Winning) + (Outcome of Losing) x (Probability of Losing)

So, we have all these variables. Now just put values into the equation of expected value.  

Expected Value =  (9$) x (1/6) + (-3$) x (5/6)

Expected Value = -1$  

It means, every time you play the game you are expected to lose 1$.

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Answer:

44. answer = a. (<)

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Step-by-step explanation:

To find the relation between the angles, we can use the law of sines in the triangle that contains both angles.

So for question 44, the angles mQRW and mRWQ are both in the triangle QWR, so we have:

10 / sin(mQRW) = 17 / sin(mRWQ)

sin(mQRW) / sin(mRWQ) = 10 / 17

The bigger the sine of the angle, the bigger the angle, so if the ratio between the sine of mQRW and sine of mRWQ is lesser than 1, the angle mQRW is lesser than the angle mRWQ (correct option: a.)

In the same way, in the question 45, the angles mRTW and mTWR are both in the triangle TWR, so we have:

15 / sin(mRTW) = 8 / sin(mTWR)

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If the ratio between the sine of mRTW and sine of mTWR is greater than 1, the angle mRTW is greater than the angle mTWR (correct option: b.)

Basically, the angle opposite to the greater side is the greater angle, and the angle opposite to the smaller side is the smaller angle.

3 0
3 years ago
What is the measure of the<br> third angle of this triangle?
Illusion [34]

Answer:

20 degrees

Step-by-step explanation:

every triangle had 3 angles that all add up to 180

the problem gives you two angles which are 120+40 which is 160

180-160 is 20 degrees which is whi it is the answer

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2 years ago
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Answer:

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Step-by-step explanation:

4 0
2 years ago
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Answer:

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Answer:

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Step-by-step explanation:

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