Question

Suppose a high school student is selected at random.Let event A = junior and event B = earbuds. Are events A and B independent

Answer 1

Events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. In this case, we need to calculate the probabilities of being a junior and using earbuds, as well as the probability of being a junior and using earbuds at the same time.

Step-by-step explanation:

In this case, event A is being a junior and event B is using earbuds. To determine if events A and B are independent, we need to determine if P(A and B) is equal to P(A) * P(B).

Here is the calculation:

P(A) = probability of being a junior = [number of juniors] / [total number of students]

P(B) = probability of using earbuds = [number of students using earbuds] / [total number of students]

P(A and B) = probability of being a junior and using earbuds = [number of juniors using earbuds] / [total number of students]

If P(A and B) is equal to P(A) * P(B), then events A and B are independent.