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by Sanjeev k Sexena » Fri Jan 17, 2014 12:48 pm
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
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by GMATGuruNY » Fri Jan 17, 2014 1:57 pm
Sanjeev k Sexena 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
The alarm only sounds for three out of four bears that actually appear at the resort.
Thus, of every 4 bears, 3 are detected by the alarm system and 1 is not.
Total number of alarms for the 3 detected bears = 3.
Since there are 10 false alarms for every undetected bear, the number of alarms yielded by the 1 undetected bear = 10.
Thus:
Of every 13 alarms, 3 are real -- implying the presence of an actual bear -- while 10 are false.
P(an alarm implies an actual bear) = 3/13.

The correct answer is B.
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