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Vaselesa [24]
3 years ago
5

A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on t

ails, then the player wins $45. Otherwise, the player wins nothing. On average, how much should a player expect to win each game
Mathematics
1 answer:
emmainna [20.7K]3 years ago
7 0

Answer:

On average, a player should expect to win $15.

Step-by-step explanation:

The expected value in an event with outcomes:

x₁, x₂, ..., xₙ

Each with probability:

p₁, ..., pₙ

is given by:

Ev = x₁*p₁ + ... +xₙ*pₙ

In this case we have 3 outcomes:

player wins $75 = x₁

player wins $45 = x₂

player does not win = x₃

Let's find the probabilities of these events.

player wins $75)

Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75

While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)

Then the number total of outcomes is:

C = 2*2*2 = 8

Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)

p₁ = 1/8

Win $45:

This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:

p₂ = 1/8

Not wining:

Remember that:

p₁ + p₂ + ... + pₙ = 1

Then for this case, we must have:

p₁ + p₂ + p₃ = 1

1/8 + 1/8 + p₃ = 1

p₃ = 1 - 1/8 - 1/8

p₃ = 6/8

Then the expected value will be:

Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15

On average, a player should expect to win $15.

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Answer:

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Step-by-step explanation:

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  3. With the same compass, still at 7cm, draw an arc centered around the left end of the line.
  4. These two arcs will intersect on either side of the line (you only need one side, so you only need a small arc in the right place, roughly where you think the third point if the triangle is.
  5. Where those arcs intersect is the third point on your triangle.  Mark that, and then trace two lines from that point to either end of the line segment you started with.

<em>You now have an equilateral triangle with 7cm sides.  Next you need to draw the circle</em>

  1. Measure the halfway point on two of your three lines.
  2. Draw a line from that each of those halfway points to the opposite corner. The new lines you're drawing will be perpendicular to the edge your measuring against.
  3. You have now drawn two line segments, and they intersect in the center of the circle.  Now take your compass and set its radius to the distance from that center point to one of the three corner points.
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Answer:

Step-by-step explanation:

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      -4 + 3x + 4 = 4x - 8 +  4

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Subtract 4x from both sides,

        3x - 4x = -4x + 4x - 4

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Divide both sides by (-5)

            \sf \dfrac{-5}{-5}x =\dfrac{10}{-5}

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    12r - 14 = 5*2 - 5*r

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 12r - 14 + 14 = 10 - 5r + 14

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Add 2x to both sides

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Divide both sides by 5

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