Answer:
Events A and B are not independent.
Step-by-step explanation:
In order for two events to be independent, the following relationship must be true:
![P(A\cap B) = P(A)*P(B)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%20%3D%20P%28A%29%2AP%28B%29)
The intersection between events A and B is the outcome that Bob and Alice have exactly one girl, the probability is:
![P(A\cap B) = 0.4*0.4*(1-0.4)\\P(A\cap B) = 0.096](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%20%3D%200.4%2A0.4%2A%281-0.4%29%5C%5CP%28A%5Ccap%20B%29%20%3D%200.096)
For event A, the possible outcomes are having one or two girls:
![P(A) = 0.4*0.4*(1-0.4)+0.4*(1-0.4)*(1-0.4)\\P(A) = 0.240](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.4%2A0.4%2A%281-0.4%29%2B0.4%2A%281-0.4%29%2A%281-0.4%29%5C%5CP%28A%29%20%3D%200.240)
For event B, the possible outcomes are having none or one girl:
![P(B) = 0.4*0.4*(1-0.4)+0.4*0.4*0.4\\P(A) = 0.16](https://tex.z-dn.net/?f=P%28B%29%20%3D%200.4%2A0.4%2A%281-0.4%29%2B0.4%2A0.4%2A0.4%5C%5CP%28A%29%20%3D%200.16)
Therefore, P(A) x P(B) is:
![P(A) *P(B)= 0.240*0.160=0.0384\\](https://tex.z-dn.net/?f=P%28A%29%20%2AP%28B%29%3D%200.240%2A0.160%3D0.0384%5C%5C)
Since P(A) x P(B) ≠ P(A∩B), events A and B are not independent
Answer:3(4x^2-9y^2)
Step-by-step explanation:
11.
Given:
There are given that the unction:
![x^2+y^2=4](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D4)
Explanation:
According to the question:
We need to fid the codition.
So,
From the given function:
![x^{2}+y^{2}=4](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%3D4)
Then,
According to the vertical line concept,
If you draw a vertical linefor any value of x in the domain, then does the vertical encounter no more than one y value.
Then,
We can say that if we do that , then we will two x values.
Final answer:
Hece, the answer is No.
Answer:
z = 1.55
Step-by-step explanation:
The answer is attached.
Answer:
189
Step-by-step explanation:
42 divide by 2 is 21
Then times 21 times 9.