Answer:
A and B are not independent events because P(A|B)≠P(A)
is the correct answer.
Step-by-step explanation:
If A and B are independent then we must have
P(AB) = P(A) P(B) and also
P(A/B) = P(A)
We are given that
A and B are two events.
Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .
P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3
i.e. P(A/B) is not equal P(A)
Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)
Hence A and B are not independent.
Answer:
Step-by-step explanation:
c + f = 10 (the coach tickets + first class tickets = 10)...there is 10 people
160c + 1230f = 6950....each coach ticket is 160 and each first class ticket is 1230.....and when added, they equal 6950 (for the airfare)
c + f = 10.....c = 10 - f
160c + 1230f = 6950
sub in 10 - f for c
160(10 - f) + 1230f = 6950
distribute the 160 thru the parenthesis
1600 - 160f + 1230f = 6950
combine like terms
1600 + 1070f = 6950
subtract 1600 from both sides
1070f = 6950 - 1600
1070f = 5350
divide both sides by 1070
f = 5350/1070
f = 5 <===== she bought 5 first class tickets
c + f = 10
we found f to be 5...so sub in 5 for f and find c, the coach tickets
c + 5 = 10
c = 10 - 5
c = 5 .......and she bought 5 coach tickets
check...
160c + 1230f = 6950
160(5) + 1230(5) = 6950
800 + 6150 = 6950
6950 = 6950 (correct)....so it checks out
5 coach and 5 first class
Option( c ) is the correct one.
-2x +y= -3
x= (3+y)/2
By executing the value in second equation
{-(3+y)/2} +2y =3
( -3-y +4y)/2 =3
-3 +3y =6
3y = 9
y = 3
Again by substituting the value of y in any of the equation
-2x +y =-3
-2x =-6
x= 3.