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 $P(Z)$

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

Step2: Calculate $P(Z|B)$

$P(Z|B)=\frac{n(Z\cap B)}{n(B)}=\frac{126}{280}=\frac{9}{20}$

Step3: Check independence

Two events $Z$ and $B$ are independent if $P(Z|B) = P(Z)$. Since $P(Z|B)=\frac{9}{20}$ and $P(Z)=\frac{9}{20}$, $Z$ and $B$ are independent events.

Answer:

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