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?  Pick one
A) 1/4
B) 3/13
C) 27/52
D) 3/4
E) 10/13
How many times the alarm goes off --&gt; 10 false + 3 true   How many of these alarms are true --&gt; 3 true alarms   Therefore, p = true alarms/total alarms = 3/13   Or, we can calculate the p (of alarm sounding but no bear detected, i.e. false alarm),   10 times when the alarm goes off - no bear is seen   13 times in all the alarm goes off   So, 10/13 is the p that alarm is a false alarm   Subtracting 10/13 from 1 is the p that it's a true alarm --&gt; (1-10/13) = 3/13....Answer 3/13
<result>B</result>
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?