Complete question :
Suppose someone gives you 8 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $8 if you succeed and you lose $2 if you fail. What is the expected value of this game to you? What can you expect if you play 100 times.
Answer:
$0.5 ; win $50 with 100 rolls
Step-by-step explanation:
From a roll of two fair dice; probability of obtaining an even number :
Even numbers = (2, 4, 6) = 3
P = 3 /6 = 1 /2
For 2 fair dice ; probability of rolling two even numbers : independent event.
1/2 * 1/2 = 1/4
Hence, p(success) = 1/4 ; P(failure) = 1 - 1/4 = 3/4
Probability table
Winning = $8 or loss = - $2
X : ____ 8 ______ - 2
P(x) __ 1/4 ______ 3/4
Expected value : E(x) = ΣX*P(x)
E(x) = (8 * 1/4) + (-2 * 3/4)
E(x) = 2 - 1.5
E(x) = $0.5
Since expected value is positive, the expect to win
If played 100 times;
Expected value = 100 * $0.5 = $50
3x+3y+6z=9
x+3y+2z=5
3x+12y+12z=18
Step 1: use Eq 2 to solve for x
x+3y+2z=5
x= -3y-2z+5
Step 2: Solve for y unsing Eq 1
3x+3y+6z=9
3y= -3x-6z+9
y= -x-2z+3
Step 3: plug in x= -3y-2z+5 to solve for the value of y
y=-x-2z+3
y= (-1)(-3y -2z +5) - 2z+3
y= 3y+2z-5- 2z+3
-2y= -2
y=1
Step 4: plug y= 1 into the x= equation
x= -3y-2z+5
x= -3(1)-2z+5
x= -2z+2
Step 5:Plug y= 1 and x= -2z+2 into the 3rd equation to solve for z
3x+12y+12z=18
12z= -3(-2z+2)-12(1)+ 18
12z= 6z - 6 - 12 +18
6z= -18+18
6z=0
z=0
Step 6: Plug z in to solve for x
x=-2z+2
x= (-2)(0)+2
x= 2
ANSWER:
x,y,z = 2,1,0
answer choice C
30s-18 is the answer jus add all the sides together/ add the like terms then solve it
(-5/3)•(-6/1)=(30/3)
(30/3) simplified is (10/1)
967.50 = 450 + 28.75p
967.50 - 450 = 28.75p
517.5 = 28.75p
18 = p
