Question

If a player rolls a die and gets a 1, he wins $5. If the person gets a 2, he wins $1. The cost to play is $2. What is the expected earning for the game?

Answer 1

Answer: $ -1

Let x be the amount the player will gain. Since the player loses $-2 each time they roll a die, we will subtract -2 from the amount the player earns.

Getting a 1 = $5 -$2

Getting a 2: $1 - $2

Getting any value that is not 1 or 2: -$2

Now, the probability of getting a 1 in a die is 1/6, which is the same as getting a 2.

The probability of getting any value that is not 1 or 2 is 4/6 (3, 4, 5, 6)

`\begin{gathered} x=(4)/(6)(-2)+(1)/(6)(5-2)+(1)/(6)(1-2) \\ x=-1 \end{gathered}`

Therefore, the expected earning for the game is $ -1