An article describes a survey of 2 096 American adults Survey participants were asked if they were football fans and also if they agreed or disagreed that the rules that the National Football Leag adopted in 2010 designed to limit head injuries have been effective Data from the survey are summarized in the table below Football Fan Not a Football Fan 1 P A Total ii P D Agree 683 199 882 Disagree Total 533 681 1 216 880 Suppose that a survey participant is to be selected at random Consider the following events A selected participant agreed that the rules have been effective D selected participant disagreed that the rules have been effective F selected participant was a football fan a Calculate the following probabilities Round your answers to four decimal places 1 214 2 096 iii P A F iv P A FC b re the events F and A independent events Justify your answer using relevant probabilities O Yes the events F and A are independent because P A F P A Yes the events F and A are independent because P AIF P A No the events F and A are not independent because P AIF P A DELAY