If we draw the contingency table of x (vertical) against y (horiz.), we have a square.
For n=4, we have (legend: < : x<y = : x=y > : x>y
y 1 2 3 4
x
1 = < < <
2 > = < <
3 > > = <
4 > > > =
We see that there are n(n-1)/2 cases of x<y out of n^2.
Therefore,
p(x<y)=n(n-1)/(2n^2)=(n-1)/(2n)
However, if the sample space is continuous, it will be simply p(x<y)=1/2.
Answer:
Step-by-step explanation:
Let that number be 
. We can build an equation, and solve for .
less than half of is 
.
more than is 
.
We are given that the two quantities are equal, so we have that 
.
Adding to both sides gives 
.
Multiplying both sides by gives 
.
Subtracting 
from both sides gives 
.
Multiplying both sides by 
gives 
.
So, the number is 
and we're done!
The check is left as an exercise to the reader.
Answer:
40
Step-by-step explanation:
Answer:
<u><em>67</em></u>
Step-by-step explanation:
<u><em>50-40+87-30</em></u>
=50+(- 40)+87(-30)
=50+87+(-40)+(-30)
=(50+87+(-40)+(-30)
=137+(-70)
=67
<u><em></em></u>
<u><em></em></u>
<u><em></em></u>
<u><em>when he wins, we add points. When he loses ,we subtract points.The score is 50 points. We right an expression to find the final score </em></u>
