Each square below represents one whole ……. What percent is represented by the shaded area?
2 answers:
Answer:
Hi, There! my name is Jay and I'm here to help!
<h2>Question</h2>What percent is represented by the shaded area?
<h2>Answer</h2>87.5 %
Step-by-step explanation:
since our denominator in 7/8 is 8, we could adjust the fraction to make the denominator 100. To do that, we divide 100 by the denominator:
100 ÷ 8 = 12.5
Once we have that, we can multiple both the numerator and denominator by this multiple:
Therefore, I hope this helps!
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The probability that all three players obtain an odd sum is 3/14.
<h3>What is probability?</h3>The probability is the ratio of possible distributions to the total distributions.
I.e.,
Probability = (possible distributions)/(total distributions)
<h3>Calculation:</h3>Given that,
There are nine tiles - 1, 2, 3,...9, respectively.
A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.
In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.
The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.
So,
One player can be selected in ways.
The 3 odd tiles out of 5 can be selected in ways.
The remaining 2 odd tiles can be selected and distributed in ways.
The remaining 4 even tiles can be equally distributed in ways.
So, the possible distributions = ×
×
×
⇒ 3 × 10 × 2 × 6 = 360
To find the total distributions,
The first player needs 3 tiles from the 9 tiles in ways
The second player needs 3 tiles from the remaining 6 tiles in ways
The third player takes the remaining tiles in 1 way.
So, the total distributions = 84 × 20 × 1 = 1680
Therefore, the required probability = (possible distributions)/(total distributions)
⇒ Probability = 360/1680 = 3/14.
So, the required probability for the three players to obtain an odd sum is 3/14.
Learn more about the probability of distributions here:
#SPJ4
Answer:
a) attached below
b) ( T,T )
c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )
d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )
while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )
Step-by-step explanation:
A) write down the game in matrix form
let: E = exit at the industry immediately
T = exit at the end of the quarter
N = exit at the end of the next quarter
matrix is attached below
B) weakly dominated strategies is ( T,T )
C) Find the pure-strategy Nash equilibria
The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )
D ) Find the unique mixed-strategy Nash equilibrium
The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )
while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE
Assume that P is the probability of firm 1 exiting immediately ( E )
and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.
hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .
The expected utilities of E and N to firm 2 =
0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3
