Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have 
and 
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of 
are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
Nancy has 54 pieces of paper, and is going to split them all between her and 5 friends. How many pieces of paper will each person receive?
Answer:
- domain: (-4, ∞)
- range: [-4, ∞)
Step-by-step explanation:
The domain is the horizontal extent of the function. This function is defined for all values of x greater than (but not including) -4. Its domain is (-4, ∞).
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The range is the vertical extent of the function. This function gives output values of any number greater than or equal to -4. Its range is [-4, ∞).
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Interval notation uses square brackets when the value is included in the interval. It uses round brackets (parentheses) when the end value is not included in the interval. ∞ is not a number, so that end always gets a round bracket.
Answer:
B shows the associative property
-5 4/5, -5.42, 5.34, 5 5/6
