Answer:
Step-by-step explanation:
1/-2
Answer:
it looks like its negative 2
Dependent events
A and B are dependent events. This means that the outcome of B affects the outcome of A.
We have that "the probability that A occurs given that B occurs" is symbolized by
P(A|B)
This is what we want to find.
We have that:
P(A): probability that event A occurs.
P(A) = 1/4
P(B): probability that event B occurs.
P(B) = 8/9
P(A&B): probability that both events A and B occurs.
P(A&B) = 1/5
We have that:
![\begin{gathered} P\mleft(A\&B\mright)=P\mleft(B\mright)\cdot P\mleft(A|B\mright) \\ \downarrow \\ \frac{P(A\&B)}{P(B)}=P(A|B) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%5Cmleft%28A%5C%26B%5Cmright%29%3DP%5Cmleft%28B%5Cmright%29%5Ccdot%20P%5Cmleft%28A%7CB%5Cmright%29%20%5C%5C%20%5Cdownarrow%20%5C%5C%20%5Cfrac%7BP%28A%5C%26B%29%7D%7BP%28B%29%7D%3DP%28A%7CB%29%20%5Cend%7Bgathered%7D)
Replacing in the equation:
![\begin{gathered} \frac{P(A\&B)}{P(B)}=P(A|B) \\ \downarrow\text{ since }P\mleft(A\&B\mright)=\frac{1}{5}\text{ and }P\mleft(B\mright)=\frac{8}{9} \\ \frac{\frac{1}{5}}{\frac{8}{9}}=P(A|B) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7BP%28A%5C%26B%29%7D%7BP%28B%29%7D%3DP%28A%7CB%29%20%5C%5C%20%5Cdownarrow%5Ctext%7B%20since%20%7DP%5Cmleft%28A%5C%26B%5Cmright%29%3D%5Cfrac%7B1%7D%7B5%7D%5Ctext%7B%20and%20%7DP%5Cmleft%28B%5Cmright%29%3D%5Cfrac%7B8%7D%7B9%7D%20%5C%5C%20%5Cfrac%7B%5Cfrac%7B1%7D%7B5%7D%7D%7B%5Cfrac%7B8%7D%7B9%7D%7D%3DP%28A%7CB%29%20%5Cend%7Bgathered%7D)
Since,
![\frac{\frac{1}{5}}{\frac{8}{9}}=\frac{1}{5}\cdot\frac{9}{8}=\frac{9}{40}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7B5%7D%7D%7B%5Cfrac%7B8%7D%7B9%7D%7D%3D%5Cfrac%7B1%7D%7B5%7D%5Ccdot%5Cfrac%7B9%7D%7B8%7D%3D%5Cfrac%7B9%7D%7B40%7D)
Then
![P(A|B)=\frac{9}{40}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7B9%7D%7B40%7D)
<h2>
Answer: 9/40</h2>
It would take Ben 60 minutes (an hour) to read 40 pages.
Answer:
[6.5,-7.25]
Step-by-step explanation:
Given the partitioning ratio as 3:1
#Find the length of the x-coordinate and multiply by the ratio:
x length=9--1=10
=>![\frac{1}{4}\times 10=2.5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Ctimes%2010%3D2.5)
#We subtract 2.5 from the x-max to get the point=9-2.5=6.5
#Find the length of the y-coordinate and multiply by the ratio:
x length=-9--2=-7
=>![\frac{1}{4}\times -7=-1.75](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20-7%3D-1.75)
#We subtract -1.75 from the y-max to get the point=-9--1.75=-7.25
Hence, the coordinates that partitions the segment into a ratio of 3 to 1 is [6.5,-7.25]