Answer:
13/19
Step-by-step explanation:
To find the reciprocal, flip the number.
The reciprocal of 19/13 is 13/19
~
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
Missing questions and subsequent solutions:
(a) Write an equation for company A for cost, C, number of months, n, that Beni will pay for the phone.
Solution:
For company A:
C = 72.25 + 85.50n
(b) Write an eqyation for company B for cost, C, and number of months, n, that Bei will pay for the phone.
Solution:
For company B:
C = 151.25 + 65.75n
(c) Write an inequality when the cost from company A is better than cost from company B.
Solution:
72.25 + 85.50n ≤ 151.25 + 65.75n
(85.50-65.75)n ≤ (151.25 - 72.25)
19.75 n ≤ 79
n ≤ 4
(d) Value of n for which cost from the two companies will be the same.
Solution:
If cost for companies A and B are the same, then
72.25 + 85.50n = 151.25 + 65.75n
(85.5 - 65.75)n = 151.25 - 72.25
19.75n = 79
n = 79/19.75 = 4 months
After 4 months,
C = 72.25 + 85.5*4 = $414.25
