An initial study was made of the use of a smartwatches with a optical sensor to detect atrial fibrillation (AF). A cohort of subjects with known risks for AF were recruited and given both a smartwatch with an app to monitor for atrial fibrillation and an ECG patch. The ECG patch also monitored for AF and collected data although it did not alert the subjects of any AF during the time period (90 days) of the study. As the participants were recruited across a wide spectrum of the population we can assume that this group os representative of the general population who share the same known risks. At the end of the study the subjects were classified by whether the smartwatch detected and alerted the subject to a possible AF or not. They were also classified by whether the ECG patch recorded actual AF or not. The table below summarises the results. WD WND Row Total ECG results AF 24 11 35 NO AF 15 39 54 Col totals 39 50 89 WD = Watch detected, the smart watch detected and notified the subject that they were experiencing AF. WND = Watch not detected, the smart watch did not detect any AF. Assuming that these proportions are representative of the whole population.) If you were to randomly pick one of the subjects what is the probability that I a. [1 mark] The person was one for whom the smartwatch detected AF OR the subject had AF (as indicated by the ECG patch) PO= b. [1 mark] The person picked had no AF detected by the watch AND the person also had no AF. PO= c. [1 mark] The person picked had AF or had No AF? PO= d. [1 mark] The person picked had No AF given that the watch detected AF? PO= e. [1 mark] The person picked had their watch detect AF given that they did not have AF? PO= f. [2 marks] Determine if we can consider the watch detecting AF and a person having AF independent or dependent events? You need to use a numerical method to show this. g. [1 mark] Give one example of two mutually exclusive events from the table