Problem Solving

Refer to the following prompt for the questions 1-2:

The bear alarm at Grizzly's Peak ski resort sounds an average of once every thirty days, but the alarm is so sensitively calibrated that it sounds an average of ten false alarms for every undetected bear. Despite this, the alarm only sounds for three out of four bears that actually appear at the resort.

1. If the alarm sounds, what is the probability that a bear has actually been sighted.
(A) 1/4
(B) 3/13
(C) 27/52
(D) 3/4
(E) 10/13

2. On any given day at the resort, what is the approximate probability that there is neither an alarm nor an undetectable bear.
(A) 224/365
(B) 13/14
(C) 14/15
(D) 376/390
(E) 29/30

Please provide explanation of your answer so as to help other members.

Source: Veritas Prep

[spoiler]OA: After some discussions[/spoiler]

Two more questions in the sequel and with the same prompt: https://www.beatthegmat.com/the-bear-ala ... 63006.html