Question

Expected Value in Games. Find the expected value​ (to you) of the described game. You are given 7 to 1 odds against rolling a double number​ (for example, two 1s or two​ 2s) with the roll of two fair​ dice, meaning you win​ $7 if you succeed and you lose​ $1 if you fail. Would you expect to win or lose money in 1​ game? In 100​ games? Explain

Answer 1

With 2 dice:

Total number of possibilities = 6 X 6 = 36

Number of possibilities of double numbers: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6): 6 Nos.

So,

p = Probabiliy of double number = 6/36 = 1/6

q = 1- p = 5/6

Event	Value for you (Random Variable x)	Probability (p) of x	xp
Rolling a double number	7	1/6	7/6
Not roolling a double number	-1	5/6	-5/6
Expected value			7/6 -5/6 = 2/6 = 0.33

(a)

In 1 game, you would expect to win money = $0.33

(b)

In 100 games, you would expect to win money = $0.33 X 100 = $33

So,

Answers to questions asked:

(a) In 1 game: win: $0.33

(b) In 100 games: win: $33