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:
1/4
Step-by-step explanation:
A I guess (finger crossed )
A function can be represented by equations and tables
- 4 users are logged in by 9am
- The domain is [3,23] and the range of the function is [3,4]
<h3>The number of users at 9am</h3>
The function is given as:
At 9am, x = 9.
So, we have:
Simplify
Approximate
Hence, 4 users are logged in by 9am
<h3>The domain</h3>
Set the radical to 0
Solve for x
The maximum time after midnight is 23 hours.
So, the domain is [3,23]
<h3>The range</h3>
When x = 3, we have:
When x = 23, we have:
So, the range of the function is [3,4]
Read more about domain and range at:
brainly.com/question/2264373
