QUESTION 1 [18 marks] Plenty of Fisher Pavlov is an eligible bachelor despite his best efforts. To gure out why, he turned to the only logical place: mathematics. Per his estimates, only i in IIIIEl1 women would malre for a suitable partner for him. In his quest to nd \"The One\d] [10 marks] Upon nding out the proportion of participants that passed the initial screening, Pavlov realized that it is still too high. He requested Plenty of Fisher's help and they agreed to conduct another independent screening with the same sensitivity and false positive rates as before. Assume that the screening results are independent. {i} [4 marks] Let passi be the event that a particular individual passes the i'" screening. Find Pllpassglpass, the probability that an individual passes the second screening given that the],I passed the rst screening. {ii} ['2 marks] Compare the probability from part {1'} with the probability of passing the rst screening only. Which is larger? Does this make sense in light of the screenings being indep-dent? Explain