Suppose it costs $43 to roll a pair of dice. you get paid $6 times the sum of the numbers that appear on the dice. is it a fair
1 answer:
The game is not fair as 6 times the expected sum is less than the cost, $43.
In the question, we are asked if the game is fair.
For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,
6E(X) ≥ 43.
The expected sum for the pair, E(X) can be calculated using the formula,
E(X) = ∑x.p(x),
or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,
or, E(X) = 107/18.
Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.
Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.
Learn more about expected return from a game at
#SPJ4
You might be interested in
We can infer and logically deduce that the arc intersected by these chords are not congruent.
<h3>What is a circle?</h3>A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
In Geometry, a circle is generally considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.
<h3>What is an arc?</h3>In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.
Let the radii of the two (2) different circles with center O and O' be r₁ and r₂ respectively. Also, two (2) isosceles triangles AOB and COD would be formed and as such we have:
AO = OB = r₁.
CO = O'D = r₂.
By critically observing the diagram (see attachment) of these circles, we can logically deduce that the arc intersected by chord AB is greater than the arc intersected by the chord CD.
This ultimately implies that, the arcs intersected by these chords are not congruent.
Read more on arcs here: brainly.com/question/11126174
#SPJ1
<u>Complete Question:</u>
Two circles with different radii have chords AB and CD, such that AB is congruent to CD. Are the arcs intersected by these chords also congruent? Explain.
Hint: It would be helpful to draw two circles and label them according to the given information, then evaluate possible arc measures.
Consider the type of triangle that may be drawn by connecting the endpoints of a chord to the center of a circle. Compare the triangles made by two circles with different radii.
