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
Answer:
A. Sin 2x
Step-by-step explanation:
This is a trig function and has the shape of sine or cosine. Since it intersects at (0,0), it is likely a sine graph. A normal sine graph starts at (0,0), crests up at 1, and crosses back down at the x-axis at (3.14, 0). However, this graph starts at (0,0) and crosses back again at half that value. This graph has been horizontally compressed by multiplication of a number greater than 1. So this graph is Sin 2x.
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Answer:
7,700
Step-by-step explanation:
-175 x 6 = -1,050
-1,050 + 8,750 = 7,700
X=amout the shirts cost
52=8+6.50+2x
add 8 and 6.5
52=14.5+2x
subtract 14.5 from 52
37.5=2x
divide 37.5 by 2
x=18.75
It cost $18.75 for each shirt.
