Double Dice is a game in which two dice are rolled. A player wins the game if a certain sum is rolled. A player wins $7.00 if he rolls a sum of 5 or 6 and $20.00 if he rolls a sum of 2 or 3. He wins nothing if any other sum is rolled. A. Define the random variable, X.
B. Write out the probability distribution function for the game.
C. What is the expected value of the game?
D. Assuming you have to pay $6.00 to play the game, explain what happens in the long run. (Is it a good idea to play the game?)

3.417

Kindly check explanation

Step-by-step explanation:

X : $7 ; $20 ; $0

Sample space for the sum of two die rolls :

Probability of obtaining a sum of 5 or 6 ;

P(sum of 5 or 6) = 9/36 = 1/4

Probability of obtaining a sum of 2 or 3 ;

P(Sum of 2 or 3) = 3/36 = 1/12

Probability of obtaining a sum of other Tha 2,3, 5 or 6 ; = 24/ 36 = 2/3

The probability distribution :

X _____ 0 _______ 7 _____ 20

P(x) ___ 2/3 _____ 1/4 ____ 1/12

Expected value of the game ; E(X) ;

E(X) = Σx*p(x)

E(X) = (0*2/3) + (7*1/4) + (20*1/12)

E(X) = 0 + 1.75 + 1.6667

E(X) = 3.417

This means that if the game is paid for a long time, the mean or expected winning will be ; $3.417

If game has to be played with $6 ; then to determine if it is a good idea to play the game on a long run, we calculate the payoff ;

The payoff is :

Expected value - playing cost

$3.417 - $6  = - $2.583

Since payoff is negative, we can conclude that it is not a good idea to play the game in the long run : as the expected value is lesser than the playing fee.

step-by-step explanation:

options

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc