Answer:
1444 uf FC fun with that one is a little bit ago and now I have to do it again in a bit of the day I will be there in a few days
Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
![1\leq x\leq 3,\quad 1\leq y \leq 5](https://tex.z-dn.net/?f=1%5Cleq%20x%5Cleq%203%2C%5Cquad%201%5Cleq%20y%20%5Cleq%205)
We have
and
, because the dice are fair.
Now we use the assumption of independence to claim that
![P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}](https://tex.z-dn.net/?f=%20P%28X%3Dx%2C%20Y%3Dy%29%20%3D%20P%28X%3Dx%29%5Ccdot%20P%28Y%3Dy%29%20%3D%5Cdfrac%7B1%7D%7B3%7D%5Ccdot%5Cdfrac%7B1%7D%7B5%7D%20%3D%20%5Cdfrac%7B1%7D%7B15%7D)
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:
A, B, D and F.
Step-by-step explanation:
Rin spends $20 every week on drum lessons.
If:
d = total amount of dollars Rin spends
w = number of weeks
Then: d=20w
w is the independent variable while d is the dependent variable. A change in w will lead to a change in d. Therefore:
(A)The independent variable causes a change in the dependent variable.
(B)The equation is d = 20w.
From the equation: d=20w
When w=1, d=$20
When w=2, d=$40
When w=3, d=$60
When w=4, d=$80
This tallys with the values in Option F.
Therefore:
(D)As the number of weeks increases, the total dollars Rin spends increases.
The correct options are: A, B, D and F.