Which statement is true about whether Z and B are independent events?
1 answer:
Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
After a small online search, I've found a table to complete this problem, that we can see below.
For two events Z and B, we have:
P(Z|B) = probability of Z given that B
such that:
P(Z|B) = P(Z∩B)/P(B)
So, two events are independent if the outcome of one does not affect the outcome of the other.
So, if the probability of Z given B is different than P(Z) (the probability of event Z) means that the events are not independent.
So Z and B are independent if the probability of Z given B is equal to the probability of Z.
P(Z|B) = P(Z)
In the table we can see:
P(Z|B) will be equal to the quotient between all the cases of Z given B (126) and the total cases are given B (280)
P(Z|B) = 126/280 = 0.45
Similarly, we can find P(Z):
And P(Z) = 297/660 = 0.45
So we can see that:
P(Z|B) = P(Z)
Thus, B and Z are independent.
You might be interested in
Answer: The base is 17 meters long, and the height is 12 meters.
Step-by-step explanation:
The area of a triangle is:
A = b*h/2
where:
b = base
h = height.
For this particular triangle, we have that:
b = 5m + h
A = 102 m^2 = b*h/2
We can replace the first equation into the second one:
b*h/2 = 102 m^2
(5m + h)*h/2 = 102 m^2
(5m + h)*h = 2*102 m^2 = 204m^2
5m*h + h^2 = 204m^2
We can rewrite this as a quadratic equation:
h^2 + 5m*h - 204m^2 = 0
The solutions are given by the Bhaskara formula, the solutions are:
Then the two solutions are:
h = (-5m - 29m)/2 = -17 m
This is a negative height, that is not really defined, so this will be discarded.
The other solution is:
h = (-5m + 29m)/2 = 12m
This is positive, so this is the option we will use.
Knowing h, we can find the value of b.
b = 5m + h = 5m + 12m = 17m
Then the area is:
A = 12m*17m/2 = 102m^2