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:
This is not a right triangle because the hypotenuse is less than the two sides and aren't equal when following the Pythagorean thm
Step-by-step explanation:
To confirm if a triangle is a right triangle, we must use the Pythagorean thm
a^2 + b^2 = c^2
23^2 + 11.4^2 = 21.2^2
529 + 129.96 = 449.44
658.96 ≠ 449.44
Answer:
Step-by-step explanation:
i think the last number 2.50 is wrong, maybe is 2.4
total cost= 0.30 x number of miles
for the first 0.30*2=0.60
second 0.30*4=1.20
and so on
Answer:
If MN = XY, and XY = AB, then MN = AB. Transitive Property
If AB = CD, then CD = AB. Symmetric Property
Segment CD is congruent to segment CD. Reflexive Property
Step-by-step explanation:
Transitive property states that for all reall numbers a, b, and c, if a = b, b = c, then a = c.
Symmetric Property states that for all real numbers a and b, if a = b, then b = a.
Reflexive Property states that for every real number a, a=a
Let w = the number of weeks you talked on your cell phone
60 min = 1 hr
60w + 250 = total number of minutes
