The bear alarm at Grizzly’s Peak ski resort sounds an aver

BTGmoderatorRO wrote: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. 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

Since the alarm only sounds for 3 out of 4 bears that actually appear at the resort, that means for every 4 bears appearing at the resort, 3 bears are detected and 1 bear is undetected. However, for every one undetected bear, there are 10 false alarms. So the number of alarms for the 3 detected bears = 3 and the number of alarms for the 1 undetected bear = 10. Thus for every 3 + 10 = 13 alarms, 3 bears will be detected, so the probability that a bear has actually been sighted, given that the alarm sounds, is 3/13.

Answer: B