Mr. White is a teaching Chemistry class in Latimer Hall. His class has 100 undergraduate staff (UGSis, tutors, etc.). Mr. White learns that one of his staff is stealing blackboard erasers from his lecture hall when the building is closed overnight. The only way the thief could access the building overnight is with a key card that belongs to them, Suppose Mr. White discovers that 10 of his staff have a key card. If Mr. White randomly selects one of his staff, what is the probability that they are the eraser thief?
0.01
0.1
0.99 . 9/99 (0.01 1)/(0.01 * 1 +0.999/99)
(011)/(0.11 +0.9.1/99)
If Mr. White randomly selects one of his staff, what is the probability that they are not the eraser thief and have a key card?
(0.01. 1)/(0.01 - 1 + 0.999/99)
0.99 * 9/99
0.99
0.01
(0.1 - 1)/(0.11 +0.9 1/99)
At the next course staff meeting, Mr. White notices that one of his GSIS, Gus, has a key card sticking out of his wallet Given this information, what is the probability that Gus is the eraser thief?
0.01
1
1
-0.99 * 9/99
(0.1 1)/(0.11 +0.9* 1/99)
(0.01 * 1)/(0.01 * 1 +0.99 * 9/99)
Mr. White is skeptical of his head GSI, Jesse. Prior to learning any information about Jesse's keycard access, Mr. White believes there is a 25% probability that Jesse is the eraser thief. Suppose Mr. White later discovers that Jesse has a key card. Given this new information, what is the probability that Jesse is the eraser thief?
0.1
(0.25. 1)/(0.251 +0.75 * 9/99)
0.25
(0.25. 9/99)/(0.259/99 +0.75 * 1)
1 -0.75 * 9/99 2