Question

select the correct answer.
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 0.67.
which statement is true?
a. events a and b are dependent because $p(a|b) = p(a)$.
b. events a and b are independent because $p(a|b) = p(a)$.
c. events a and b are dependent because $p(a|b) \
eq p(a)$.
d. events a and b are independent because $p(a|b) = p(b)$.

Explanation:

Step1: Recall independence definition

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

Step2: Compare given probabilities

We know $P(A) = 0.67$ and $P(A|B) = 0.67$, so $P(A|B) = P(A)$.

Step3: Match to correct statement

This equality satisfies the condition for independent events.

Answer:

B. Events A and B are independent because $P(A|B) = P(A)$.