4. Finding an organ transplant match. Only if the antigens attached to the tissue cells of the donor and receiver match, the body will accept the transplanted tissue. Antigens in identical twins always match, the probability of a match in other siblings is 0.25, and the probability of the match in two people from the population at large is 0.001. Suppose that you need a kidney and you have 2 brothers and a sister. a) If one of your three siblings offers a kidney, what is the probability that the antigens will match? b) If all the three siblings offer a kidney, what is the probability that all three antigens will match? 0) If all the three siblings offer a kidney, what is the probability that none three antigens will match? d) Assuming that the three donors were obtained form the population at large, what is the probability that all three antigens will match? 1. Elderly wheelchair user study. A sample of 306 wheelchairs users, age 65 or alder, were surveyed about they had an injurious fall during the year and whether their home featured any of 5 selected structural modications. The responses are summarized in the table below. Home Features Injurious Fall(s) No Falls Totals A115 2 7 9 At least 1, but not all 26 162 188 None 20 89 109 Totals 48 258 306 a) Find the probability that the wheelchair used had an injurious fall. b) Find the probability that the wheelchair used had all ve features installed at home c) Find the probability that the wheelchair used had no falls and none of the features installed at home d) Given no features installed in the home, nd the probability of an injurious fall. 2. A state senator believes that 20% of all senators on the Finance Committee will strongly support the tax proposal she wishes to advance. Suppose that this believes is correct and that 5 senators are approached at random. What is the probability that less than 2 of them will strongly support the prOposal? 3. Given "=9 , and probability of success of 0.8, nd the probability that: a) X is greater than or equals to 4 b) X is exactly 5. c) X is at least 3 but no more than 7