<span>x = child ticket price
y = adult ticket price
5x+3y=52 the cost accounting for the first group.
3x+2y=38 the cost accounting for the second group.
Child price: 5$
Adult price: 9$</span>
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:
<u>262,144</u> goes in the blank
Step-by-step explanation:
8^6 = 262,144
4^11 = 4,194,304
4,194,304 + 262,144 = 4,456,448
4,456,448 ÷ 17 = 262,144
Answer:
16 times
Step-by-step explanation:
13 + 4 +8 = 25 total marbles
(4 is total number of blue marbles, 25 is complete total of marbles)
4/25 times = ?/100 times
Because 25 times 4 is equal to 100, you then multiply 4 by 4 to get 16
16/100 times
