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
The general formula for the lateral surface area of a right prism is
L = ph
where p represents the perimeter of the base and h represents the height of the prism.
In our case, the perimeter is the sum of the bases.
p = 5 + 5.6 + 2.5 = 13.1 cm
now, the height of the prism is 8 cm
then L = 13.1 cm x 8 cm = 104.8cm^2
Answer:
No, modern train cannot travel on old railroad.
Step-by-step explanation:
In rail transport, track gauge is the spacing of the rails on a railway track and is measured between the inner faces of the load-bearing rails.
Most of the modern train are based on broad gauge. The separation in broad gauge is about 5 ft and 6 inches and in the standard gauge the separation between the tracks is 4 ft and 
inches. So for the modern train it is not possible to travel on the tracks whose separation is no more than 4.5 feet.
I believe this is pythag
15^2 x 11^2 = 27225
(square root) of 27225 = 165
165ft
Answer:
it is a 30 degree angle
Step-by-step explanation:
