Part 1: Jack has strep throat. The probability of a quick recovery for those with strep is 50%. For those with a resistant strain of strep who are untreated the probability of a quick recovery is 10%. For those with a non-resistant strain who are treated with penicillin, the likelihood of a quick recovery is 20%. It turns out that Jack has a resistant strain, and Jack's doctor decides to not treat him. Fortunately, Jack recovers quickly. Does Jack's doctor's decision help explain his quick recovery?
Part 2: Jack's identical twin brother Mack has a non-resistant form of strep, and his doctor also decides not to treat him. Unfortunately, he recovery is quite slow. Does Mack's doctor's decision help explain his slow recovery?