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

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).

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).

Answer

Explanation:

Step1: Calculate $P(Z)$

$P(Z)=\frac{\text{Number of }Z}{\text{Total}}=\frac{297}{660}=\frac{9}{20} = 0.45$

Step2: Calculate $P(Z|B)$

$P(Z|B)=\frac{\text{Number of }Z\text{ and }B}{\text{Number of }B}=\frac{126}{280}=\frac{9}{20}= 0.45$

Step3: Check independence condition

Two events $Z$ and $B$ are independent if $P(Z|B)=P(Z)$. Since $P(Z|B) = 0.45$ and $P(Z)=0.45$, they are independent.

Answer:

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