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An airport screens bags for forbidden items, and an alarm is supposed

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An airport screens bags for forbidden items, and an alarm is supposed  [#permalink]

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New post 14 Apr 2019, 02:52
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  55% (hard)

Question Stats:

39% (01:54) correct 61% (01:46) wrong based on 18 sessions

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An airport screens bags for forbidden items and an alarm is supposed to be triggered when a forbidden item is detected. Suppose that 5% of bags contain forbidden items. Given a randomly chosen bag triggers the alarm, what is the probability that it contains a forbidden item?

A) If a bag contains a forbidden item, there is a 98% chance that it triggers the alarm.

B) If a bag doesn't contain a forbidden item, there is an 8% chance that it triggers the alarm.

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Re: An airport screens bags for forbidden items, and an alarm is supposed  [#permalink]

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New post 14 Apr 2019, 07:06
Pl provide the solution also.
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Re: An airport screens bags for forbidden items, and an alarm is supposed  [#permalink]

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New post 14 Apr 2019, 08:19
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eswarchethu135 wrote:
An airport screens bags for forbidden items and an alarm is supposed to be triggered when a forbidden item is detected. Suppose that 5% of bags contain forbidden items. Given a randomly chosen bag triggers the alarm, what is the probability that it contains a forbidden item?

A) If a bag contains a forbidden item, there is a 98% chance that it triggers the alarm.

B) If a bag doesn't contain a forbidden item, there is an 8% chance that it triggers the alarm.


So the alarm bell has been triggered..
Now there are two cases - genuine ( let the prob be g) and false ( let the probability be f)
So our answer will be based on two cases that the bell has already triggered..
Incase of genuine cases - (5% forbidden )*g
Incase of false cases -(95% clean baggage)*f
Probability = (5% forbidden )*g/((5% forbidden )*g +(95% clean baggage)*f)

Thus we are looking for value of g and f..
Statement I tells us g is 0.98 and statement II tells us that f is 0.08..
Thus probability =0.05*0.98/( 0.05*0.98+0.08*0.95)

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Re: An airport screens bags for forbidden items, and an alarm is supposed   [#permalink] 14 Apr 2019, 08:19
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