Question

the probability that edward purchases a video game from a store is 0.67 (event a), and the probability that greg purchases a video game from the store is 0.74 (event b). the probability that edward purchases a video game (given that greg has purchased a video game) is 0.87. which statement is true? a. events a and b are dependent because p(a|b) = p(a) b. events a and b are dependent because p(a|b) ≠ p(a) c. events a and b are independent because p(a|b) = p(a) d. events a and b are independent because p(a|b) = p(b)

Explanation:

Step1: Recall the definition of independent and dependent events

Two events $A$ and $B$ are independent if $P(A|B)=P(A)$, and dependent if $P(A|B)
eq P(A)$.

Step2: Identify the given probabilities

We are given that $P(A) = 0.67$, $P(B)=0.74$ and $P(A|B)=0.87$.

Step3: Compare the probabilities

Since $P(A|B)=0.87$ and $P(A) = 0.67$, we have $P(A|B)
eq P(A)$. So events $A$ and $B$ are dependent.

Answer:

B. Events A and B are dependent because $P(A|B)
eq P(A)$