1. A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and without replacement. Calculate the probability that the number of boys selected exceeds the number of girls selected.
2. Upon arrival at a hospital's emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year:

(i) 20% of the emergency room patients were critical;

(ii) 40% of the emergency room patients were serious;

(iii) the rest of the emergency room patients were stable; (iv) 50% of the critical patients died;

(vi) 5% of the serious patients died; and

(vii) 1% of the stable patients died.

Given that a patient survived, calculate the probability that the patient was categorized as critical upon arrival.