In a quiz contest, Mary answers 90% of the questions correctly without any additional clues from the quiz coordinator. The randomly generated numbers below simulate this situation. The numbers 0 to 8 represent questions answered correctly without additional clues, and the number 9 represents questions that needed additional clues.

To solve this problem, we should note that there are:

total questions = 100

questions answered correctly = 90

questions that needed additional clues = 10

1. The first question is to find the probability that in the third question, Mary would need additional clue. Therefore this implies that in the first and second questions, Mary would answer it correctly. Therefore:

Probability = (question 1 answered correctly) * (question 2 answered correctly) * (question 3 needed clue)

Probability = (90/100) * (89/99) * (10/98)

Probability = 0.08256 = 8.26%

2. The second question finds for the probability that two consecutive needs additional clue, therefore:

Probability = (question 1 needed clue) * (question 2 needed clue)

Probability = (10/100) * (9/99)

Probability = 9.1*10^-3 = 0.91%