Answer:Given:
P(A)=1/400
P(B|A)=9/10
P(B|~A)=1/10
By the law of complements,
P(~A)=1-P(A)=399/400
By the law of total probability,
P(B)=P(B|A)*P(A)+P(B|A)*P(~A)
=(9/10)*(1/400)+(1/10)*(399/400)
=51/500
Note: get used to working in fraction when doing probability.
(a) Find P(A|B):
By Baye's Theorem,
P(A|B)
=P(B|A)*P(A)/P(B)
=(9/10)*(1/400)/(51/500)
=3/136
(b) Find P(~A|~B)
We know that
P(~A)=1-P(A)=399/400
P(~B)=1-P(B)=133/136
P(A∩B)
=P(B|A)*P(A) [def. of cond. prob.]
=9/10*(1/400)
=9/4000
P(A∪B)
=P(A)+P(B)-P(A∩B)
=1/400+51/500-9/4000
=409/4000
P(~A|~B)
=P(~A∩~B)/P(~B)
=P(~A∪B)/P(~B)
=(1-P(A∪B)/(1-P(B)) [ law of complements ]
=(3591/4000) ÷ (449/500)
=3591/3592
The results can be easily verified using a contingency table for a random sample of 4000 persons (assuming outcomes correspond exactly to probability):
===....B...~B...TOT
..A . 9 . . 1 . . 10
.~A .399 .3591 . 3990
Tot .408 .3592 . 4000
So P(A|B)=9/408=3/136
P(~A|~B)=3591/3592
As before.
Step-by-step explanation: its were the answer is
Answer:
The first step is to replace the y in y-x=15 with 7x (we can do this because the first equation tells us that they're equal)
solve and get
(2.5,17.5)
or x= 2.5 y=17.5
Step-by-step explanation:
The first step is to recognize that y=7x which means that we can just replace the y in the second equation with 7x
7x-x=15
6x=15
x=2.5
Then we can solve for y
y=7(2.5)
y=17.5
The lowest common denominator is 21
![3xy \sqrt[24]{ {4x}^{2} }](https://tex.z-dn.net/?f=3xy%20%5Csqrt%5B24%5D%7B%20%7B4x%7D%5E%7B2%7D%20%7D%20)
(3xy^2 4 sqrt 4x^2)
Step-by-step explanation:
<h3>Hope it's helpful to you</h3>
I think k equals negative 2, or -2.<span>
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