Game: roll two die. win a prize based off the sum of the die rolled.
cost of playing the game is $1
prizes:
-win $10 if your sum is odd.
-win $5 if you roll a sum of 4 or 8.
-win $50 if you roll a sum of 2 or 12.
explain how to find the expected value of playing this game. what is the expected value of playing this game? show your work.
interpret the meaning of the expected value in the context of this game. why should someone play or not play this game? give your answer in complete sentences.

Let be the random variable representing the winnings you get for playing the game. Then

First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.

So the probability mass function for this game is

The expected value of playing the game is then

or about $7.89.

The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

it is a. 4.2 because 7.6-3.4 gets the remaining length of 4.2. i might be wrong but i am pretty sure this is the answer.