Answer:
Average grade for this test = 1.85
Step-by-step explanation:
Given that number of students receiving respective grade scores are : 11, 18, 52, 13, 6
Then total number of students = 11 + 18 + 52 + 13 + 6 = 100
Sum score obtained by total students
= 11F + 18D + 52C + 13B + 6A
= 11(0) + 18(1) + 52(2) + 13(3) + 6(4)
= 0 + 18 + 104 + 39 + 24
= 185
Now average grade for this test is given by 185/100 = 1.85
Hence final answer is 1.85.
Answer:
Mr. Peterson
Step-by-step explanation:
u and one
Answer:
<u>For probabilities with replacement</u>




<u>For probabilities without replacement</u>




Step-by-step explanation:
Given



<u>For probabilities with replacement</u>
(a) P(2 Red)
This is calculated as:


So, we have:



(b) P(2 Black)
This is calculated as:


So, we have:



(c) P(1 Red and 1 Black)
This is calculated as:
![P(1\ Red\ and\ 1\ Black) = [P(Red)\ and\ P(Black)]\ or\ [P(Black)\ and\ P(Red)]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5BP%28Red%29%5C%20and%5C%20P%28Black%29%5D%5C%20or%5C%20%5BP%28Black%29%5C%20and%5C%20P%28Red%29%5D)
![P(1\ Red\ and\ 1\ Black) = [P(Red)\ *\ P(Black)]\ +\ [P(Black)\ *\ P(Red)]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5BP%28Red%29%5C%20%2A%5C%20P%28Black%29%5D%5C%20%2B%5C%20%5BP%28Black%29%5C%20%2A%5C%20P%28Red%29%5D)
![P(1\ Red\ and\ 1\ Black) = 2[P(Red)\ *\ P(Black)]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%202%5BP%28Red%29%5C%20%2A%5C%20P%28Black%29%5D)
So, we have:
![P(1\ Red\ and\ 1\ Black) = 2*[\frac{5}{8} *\frac{3}{8}]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%202%2A%5B%5Cfrac%7B5%7D%7B8%7D%20%2A%5Cfrac%7B3%7D%7B8%7D%5D)


(d) P(1st Red and 2nd Black)
This is calculated as:
![P(1st\ Red\ and\ 2nd\ Black) = [P(Red)\ and\ P(Black)]](https://tex.z-dn.net/?f=P%281st%5C%20Red%5C%20and%5C%202nd%5C%20Black%29%20%3D%20%5BP%28Red%29%5C%20and%5C%20P%28Black%29%5D)


So, we have:


<u></u>
<u>For probabilities without replacement</u>
(a) P(2 Red)
This is calculated as:


So, we have:

<em>We subtracted 1 because the number of red balls (and the total) decreased by 1 after the first red ball is picked.</em>



(b) P(2 Black)
This is calculated as:


So, we have:

<em>We subtracted 1 because the number of black balls (and the total) decreased by 1 after the first black ball is picked.</em>



(c) P(1 Red and 1 Black)
This is calculated as:
![P(1\ Red\ and\ 1\ Black) = [P(Red)\ and\ P(Black)]\ or\ [P(Black)\ and\ P(Red)]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5BP%28Red%29%5C%20and%5C%20P%28Black%29%5D%5C%20or%5C%20%5BP%28Black%29%5C%20and%5C%20P%28Red%29%5D)
![P(1\ Red\ and\ 1\ Black) = [P(Red)\ *\ P(Black)]\ +\ [P(Black)\ *\ P(Red)]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5BP%28Red%29%5C%20%2A%5C%20P%28Black%29%5D%5C%20%2B%5C%20%5BP%28Black%29%5C%20%2A%5C%20P%28Red%29%5D)
![P(1\ Red\ and\ 1\ Black) = [\frac{n(Red)}{Total}\ *\ \frac{n(Black)}{Total-1}]\ +\ [\frac{n(Black)}{Total}\ *\ \frac{n(Red)}{Total-1}]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5B%5Cfrac%7Bn%28Red%29%7D%7BTotal%7D%5C%20%2A%5C%20%5Cfrac%7Bn%28Black%29%7D%7BTotal-1%7D%5D%5C%20%2B%5C%20%5B%5Cfrac%7Bn%28Black%29%7D%7BTotal%7D%5C%20%2A%5C%20%5Cfrac%7Bn%28Red%29%7D%7BTotal-1%7D%5D)
So, we have:
![P(1\ Red\ and\ 1\ Black) = [\frac{5}{8} *\frac{3}{7}] + [\frac{3}{8} *\frac{5}{7}]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5B%5Cfrac%7B5%7D%7B8%7D%20%2A%5Cfrac%7B3%7D%7B7%7D%5D%20%2B%20%5B%5Cfrac%7B3%7D%7B8%7D%20%2A%5Cfrac%7B5%7D%7B7%7D%5D)
![P(1\ Red\ and\ 1\ Black) = [\frac{15}{56} ] + [\frac{15}{56}]](https://tex.z-dn.net/?f=P%281%5C%20Red%5C%20and%5C%201%5C%20Black%29%20%3D%20%5B%5Cfrac%7B15%7D%7B56%7D%20%5D%20%2B%20%5B%5Cfrac%7B15%7D%7B56%7D%5D)


(d) P(1st Red and 2nd Black)
This is calculated as:
![P(1st\ Red\ and\ 2nd\ Black) = [P(Red)\ and\ P(Black)]](https://tex.z-dn.net/?f=P%281st%5C%20Red%5C%20and%5C%202nd%5C%20Black%29%20%3D%20%5BP%28Red%29%5C%20and%5C%20P%28Black%29%5D)


So, we have:


Answer:
x ∈ (-oo ; 3)
Step-by-step explanation:
4x - 7 < 5
4x < 5 + 7
4x < 12
x < 12 : 4
x < 3
x ∈ (-oo ; 3)