which statement is true about whether z and b are independent events?\nz and b are independent events…

which statement is true about whether z and b are independent events?\nz and b are independent events because p(z | b) = p(z).\nz and b are independent events because p(z | b) = p(b).\nz and b are not independent events because p(z | b) ≠ p(z).\nz and b are not independent events because p(z | b) ≠ p(b).

which statement is true about whether z and b are independent events?\nz and b are independent events because p(z | b) = p(z).\nz and b are independent events because p(z | b) = p(b).\nz and b are not independent events because p(z | b) ≠ p(z).\nz and b are not independent events because p(z | b) ≠ p(b).

Answer

Explanation:

Step1: Calculate $P(Z)$

The total number of outcomes is $n = 660$, and the number of times $Z$ occurs is $297$. So $P(Z)=\frac{297}{660}=\frac{9}{20}= 0.45$.

Step2: Calculate $P(Z|B)$

The formula for conditional - probability is $P(Z|B)=\frac{P(Z\cap B)}{P(B)}$. The number of elements in $Z\cap B$ is $126$, and the number of elements in $B$ is $280$. So $P(Z|B)=\frac{126}{280}=\frac{9}{20}=0.45$.

Answer:

Z and B are independent events because $P(Z | B)=P(Z)$.