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slava
3 months ago
13

Two players A and B play a marble game. Each player has both a red and blue marble. They present one marble to each other. If bo

th present red, A wins $3. If both present blue, A wins $1. If the colors of the two marbles do not match, B wins $2. Is it better to be A, or B, or does it matter?
Mathematics
1 answer:
Zina [12.3K]3 months ago
5 0

Answer:

Step-by-step explanation:

Player A has a red marble and a blue marble, while Player B also has a red marble and a blue marble.

Therefore, the probability of selecting one marble is equal, at 0.5.

Due to the independence of A and B's choices, the joint event is calculated by multiplying the probabilities.

Let A represent the amount that player A wins.

If both players select one marble, the sample space can be considered as

             (R,R)  (R,B)  (B,R) (B,B)

Probability     0.25  0.25  0.25  0.25

A's winnings          3       -2     -2       1

E(A)      0.75   -0.5    -0.5   0.25   =    0

Thus, the game is even, offering equal expected values for both A and B.

It does not influence the outcome whether you are A or B.

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3 months ago
CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
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Answer:

15.7 inches

Step-by-step breakdown:

A slice of a round pie is a sector of a circle.

The perimeter of a slice equals the arc length s plus two times the radius r. P = s + 2r

s = rθ = r(16/360) = r/22.5. Therefore,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

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Thus, the diameter of the cake should be 15.7 inches.

Verification:

\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}

It is accurate.

 

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2 months ago
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Answer:

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Let the area of the larger square be denoted as x

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The domain refers to the possible values that x can assume in a function

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The area of the larger square must exceed 10cm^2

The domain will consist of all real numbers greater than 10

Mathematically, R>10 indicates the required domain.

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