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:
11/ 42. *. X^ 2. * X = I/3 X A * h; if E = 1/3 A
Then the answer is EX
Step-by-step explanation:
Volume of cone= 1/3 * base area * height
= 1/3 * pi* (X/2)^2 * X
= 1/3. * 22/ 7 * X^3/4
= 22/ 21 * X^3 / 4
= 11/21 *. X^2/ 2. *. X
= 11/ 42. * X^3
= 11/ 42. *. X^ 2. * X
Answer:
90
Step-by-step explanation:
The first term = 6* 2^0 = 6
The second term = 6 * 2^ (2-1) = 6*2 = 12
The third term = 6* 2^(3-1) = 6*2^2 = 6*4 = 24
The fourth term = 6* 2^(4-1) = 6* 2^3 = 6*8 = 48
S4 is the sum of the 1st four terms
S4 = 6+ 12+24+ 48 = 90
$1040.00
______________________________________________
Raphael paid $624
624/.60= 1040.00
