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

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Intern
Joined: 28 May 2014
Posts: 34
GMAT Date: 08-20-2014
The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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25 Jul 2014, 18:29
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65% (hard)

Question Stats:

59% (01:32) correct 41% (02:06) wrong based on 144 sessions

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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
[Reveal] Spoiler: OA
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Schools: Ross (Michigan) - Class of 2017
GMAT 1: 620 Q48 V27
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Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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25 Jul 2014, 23:03
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Gmatbattle 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

Kudofy Plz

Ratio of False Alarms to Undetected Bears: $$10:1$$

Ratio of Detected Bears to Undetected Bears: $$3:1$$

Combine both Ratios: $$10:1:3$$

Probability of Detecting an actual bear: $$\frac{3}{13}$$

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Joined: 18 Sep 2014
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Location: India
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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11 Jun 2015, 08:34
justbequiet wrote:
Gmatbattle 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

Kudofy Plz

Ratio of False Alarms to Undetected Bears: $$10:1$$

Ratio of Detected Bears to Undetected Bears: $$3:1$$

Combine both Ratios: $$10:1:3$$

Probability of Detecting an actual bear: $$\frac{3}{13}$$

how did you get the Ratio of Detected Bears to Undetected Bears as : $$3:1$$
can someone explain
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Intern
Joined: 04 May 2014
Posts: 30
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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11 Jun 2015, 14:33
Mechmeera wrote:
justbequiet wrote:
Gmatbattle 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

Kudofy Plz

Ratio of False Alarms to Undetected Bears: $$10:1$$

Ratio of Detected Bears to Undetected Bears: $$3:1$$

Combine both Ratios: $$10:1:3$$

Probability of Detecting an actual bear: $$\frac{3}{13}$$

how did you get the Ratio of Detected Bears to Undetected Bears as : $$3:1$$
can someone explain

This is because there are 4 bears, but one of them is undetected, hence the ratio of 3:1 For every 3 detected, there is 1 undetected.
Hope it helps
Intern
Joined: 24 Mar 2013
Posts: 28
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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03 Jul 2015, 18:08
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We need to find p(of a true bear sighting when the alarm goes off)...
How many times the alarm goes off --> 10 false + 3 true
How many of these alarms are true --> 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 --> (1-10/13) = 3/13....Answer B
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Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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18 Oct 2017, 19:27
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Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag [#permalink]

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19 Oct 2017, 10:02
Can someone please post a simpler solution. I am unable to understand the explanantion.
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag   [#permalink] 19 Oct 2017, 10:02
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