Answer:
Step-by-step explanation:
Given
Recursive:
Required
Determine the formula
Substitute 2 for n to determine
Substitute
Next is to determine the common difference, d;
The nth term of an arithmetic sequence is calculated as
Substitute and
Hence, the nth term of the sequence can be calculated using
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.