Asimple game goes as follows: you pay one dollar and roll a die. if the roll is either a 1 or 2, you get your dollar back. if it is greater than 3 you lose the dollar you paid. if it is a 3, you get your dollar back and an additional dollar. what is the expected value of the net amount of money you win/lose?

-1/3

Step-by-step explanation:

Given that a simple game goes as follows: you pay one dollar and roll a die. If the roll is either a 1 or 2, you get your dollar back. If it is greater than 3 you lose the dollar you paid. If it is a 3, you get your dollar back and an additional dollar.

Your fee for the dollar would be 1 dollar always

If you roll 1 or 2, your gain is 0

If you roll 3, your gain is 1

If you roll 4 or 5 or 6you lose 1 dollar

Let X be the amount of gain.

X       0        1         -1

P       2/6     1/6      3/6  

E(x) = Sum of products of x with probabilities

=

Note:  this is not a fair game to play since expected gain is negative.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.