Which statement is true about whether Z and B are independent events? Z and B are independent events because P(Z∣B) = P(Z).
Z and B are independent events because P(Z∣B) = P(B).
Z and B are not independent events because P(Z∣B) ≠ P(Z).
Z and B are not independent events because P(Z∣B) ≠ P(B).

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.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or