Question

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)
eq p(z) ). z and b are not independent events because ( p(z | b)
eq p(b) ).

Explanation:

Step1: Calculate \(P(Z)\)

The formula for probability is \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For \(P(Z)\), the number of favorable outcomes (total for \(Z\)) is \(297\), and the total number of outcomes is \(660\).
So, \(P(Z)=\frac{297}{660}=\frac{9}{20} = 0.45\)

Step2: Calculate \(P(Z|B)\)

The formula for conditional probability is \(P(Z|B)=\frac{P(Z\cap B)}{P(B)}\).
\(P(Z\cap B)=\frac{126}{660}\), and \(P(B)=\frac{280}{660}\)
Then \(P(Z|B)=\frac{\frac{126}{660}}{\frac{280}{660}}=\frac{126}{280}=\frac{9}{20}= 0.45\)

Answer:

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