PLEASE HELP ME
2 answers:
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Not sure why such an old question is showing up on my feed...
Anyway, let
and 
. Then we want to find the exact value of 
.
Use the angle difference identity:
and right away we find
. By the Pythagorean theorem, we also find 
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if
, then (by Pythagorean theorem) 
, so 
. And from this, 
.
So,
Anyway, let
Use the angle difference identity:
and right away we find
Meanwhile, if
So,
Answers:
P(A) = 7/12
P(B) = 1/4
====================================================
Explanation:
Instead of having one die, let's say we have two dice. I'll make one red and the other blue.
I'll be using the dice chart shown below. The red and blue values add up to the black numbers inside the table. For instance, we have 1+1 = 2 in the upper left corner. There are 6*6 = 36 sums total.
Using that table, we can see the following:
- There are 6 copies of "7"
- There are 5 copies of "8"
- There are 4 copies of "9"
- There are 3 copies of "10"
- There are 2 copies of "11"
- There is 1 copy of "12"
In total, we have 6+5+4+3+2+1 = 21 instances where the two dice add to something larger than 6.
This is out of 36 ways to roll two dice.
Therefore P(A) = 21/36 = (3*7)/(3*12) = 7/12
-----------------------------------
If a number is divisible by 4, then it is a multiple of 4.
The multiples of 4 found in the table are: 4, 8, 12
We have
- 3 copies of "4"
- 5 copies of "8"
- 1 copy of "12"
This gives 1+5+3 = 9 values that are a multiple of 4
P(B) = 9/36 = (1*9)/(4*9) = 1/4
