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Here is the complete question.
1). What are the odds for rolling a sum of 5 in a single roll of two fair dice?
2). If you bet $1 that a sum of 5 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 5 turns up in order for the game to be fair?
Answer:
1).
2). $8.
Step-by-step explanation:
1).
The sample space (S) for rolling two fair dice is given as the following parameters illustrated below:
Let F represent the event that the sum of both dice turns up is 5.
F = [(1,4),(2,3),(3,2),(4,1)}
∴ The probability for an event F is illustrated below as:
=
2). From above, we can see that the probability for rolling a sum of 5 are 1 to 8. Therefore, if you roll a sum of 5, in order for the game to be fair, the house is required to pay $8.