Question

3. It is currently Season 8 of Game of Thrones. Before the season started one analyst came up with the following probabilities (listed in the table below) the character Slance Rinister will die in each of the 6 episodes. ** To avoid any spoilers the name of the character used has been changed for this lab. (There is in fact no character called Slance Rinister). Episode Number Slance Dies Probability of Slance Death in the episode 0.05 0.06 0.1 0.2 0.2 0.25 (a) Before the season started what did this analyst think was the probability Slance Rinister lives through b) Now we are 3 episodes into season 8 in Game of Thrones. At this point we know Slance Rinister is still the end of the show? alive. What is the conditional probability Slance Rinister lives through the end of the show?

Answer 1

$a.\ P(lives\ through) = P(\ does\ not\ die) = 1 - (sum\ of\ all\ probabilities) = 1 - 0.86 = 0.14 \\ b. \ P(lives\ through | 3rd\ show\ alive) = \frac{P(lives\ through \cap 3rd\ show\ alive)}{P(3rd\ show\ alive)} = \frac{1-(0.2+0.2+0.25)}{1-(0.05+0.06+0.1)} = 0.443$