Israeli Data: August 15,2021 From: https://datadashboard.health.gov.il/COVID-19/general Age Population (%) Severe cases Efficacy Not Vax Fully Vax Not Vax Fully Vax vs. severe disease % % per 100k per 100k All ages 1,302,912 5,634,634 214 301 67.5% 18.2% 78.7% 16.4 5.3 50 186,078 2,133,516 171 290 85.2% 7.9% 90.4% 91.9 13.6 This strange result illustrates something called Simpson's Paradox, in this case meaning you can have very high efficacy in each group, but the overall efficacy looks much lower because one group (older people) is more vaccinated and has a much higher risk of severe disease.(a) (4 points) Use the table below to calculate the conditional probability that a person under 50 in Israel was suffering from a severe case of Covid on August 15, 2021 given that the person was fully vaccinated by that date. (b) (4 points) Answer the same question as in (a) with "fully vaccinated" replaced by "not vaccinated". (c) (2 points) The efficacy of the vaccine for people under 50 in Israel is defined to be (100%) answer to (a) 1 answer to (b) Verify that the efficacy is 91.8%, as claimed