the probability that a randomly selected adult in a particular community is a smoker is 18%. the probability…

the probability that a randomly selected adult in a particular community is a smoker is 18%. the probability that a randomly selected adult in the community is a smoker, given that the adult earns more than $75,000 per year, is 18%. are the events “is a smoker” and “earns more than $75,000 per year” independent? explain. choose the correct answer below. a. yes, because it is possible for an adult in the community to be a smoker and earn over $75,000 per year, the events are independent. b. no, because it is possible for an adult in the community to be a smoker and earn over $75,000 per year, the events are not independent. c. no, because the probability of smoking is the same, even when the income condition is added, the two events are not independent. d. yes, because the probability of smoking is the same, even when the income condition is added, the two events are independent.

the probability that a randomly selected adult in a particular community is a smoker is 18%. the probability that a randomly selected adult in the community is a smoker, given that the adult earns more than $75,000 per year, is 18%. are the events “is a smoker” and “earns more than $75,000 per year” independent? explain. choose the correct answer below. a. yes, because it is possible for an adult in the community to be a smoker and earn over $75,000 per year, the events are independent. b. no, because it is possible for an adult in the community to be a smoker and earn over $75,000 per year, the events are not independent. c. no, because the probability of smoking is the same, even when the income condition is added, the two events are not independent. d. yes, because the probability of smoking is the same, even when the income condition is added, the two events are independent.

Answer

Brief Explanations:

Two events A and B are independent if the probability of event A occurring is not affected by the occurrence or non - occurrence of event B. Let A be the event "is a smoker" and B be the event "earns more than $75,000 per year". The probability of A is P(A)=0.18, and the conditional probability P(A|B) = 0.18. Since P(A)=P(A|B), the probability of being a smoker does not change when we know the income condition.

Answer:

D. Yes, because the probability of smoking is the same, even when the income condition is added, the two events are independent.