00 Homework Progress
32 / 35 Marka
Question Progress
14 Marks
There are 25 questions in a quiz.
Every correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores O points.
It is possible to finish the quiz with a negative score.
a) What is the maximum score you could get on the quiz?
75
b) What is the minimum score you could get on the quiz?
30
c) A student answers 15 questions.
10 are correct. How many points does he score?
d) Another student answers 21 questions.
6 are correct. How many points does she score?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.