4. would your prediction of whether or not a student participates in an after-school athletics program change if you knew the gender of the student? explain your answer.
two events are independent if knowing that one event has occurred does not change the probability that the otherevent has occurred. for example, consider the following two events:
: the event that a randomly selected student is female
: the event that a randomly selected student participates in an after-school athletics program
events and would be independent if the probability that a randomly selected student participates in an after-school athletics program is equal to the probability that a randomly
selected student who is female participates in an afterschool athletics program. if this was the case, knowing that a randomly selected student is female does not change the probability
that the selected student participates in an after-school athletics program. then, and would be independent.