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
Answer: 19
Reasoning: the equation is 7 + (6 x 2) = 19
Let's begin by listing out the information given to us:
8 am
airplane #1: x = 80870 ft, v = -450 ft/ min
airplane #2: x = 5000 ft, v = 900ft/min
1.
We must note that the airplanes are moving at a constant speed. The equation for the airplanes is given by:
2.
We equate equations 1 & 2 to get the time both airlanes will be at the same elevation. We have:
3.
The elevation at that time (when the elevations of the two airplanes are the same) is given by substituting the value of time into equations 1 & 2. We have:
If you look in a table of sines, you find that sin(θ) = 0.45 corresponds to an angle of about 26°45', so is nearest to 27°.
