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The oasis output of Abu Ilan in the heart of the Negev desert, has a
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Bunuel
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The oasis output of Abu Ilan in the heart of the Negev desert, has a [#permalink] New post  28 Jan 2021, 03:09
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The oasis output of Abu Ilan in the heart of the Negev desert, has a population of 20 Bedouin tribesmen and 20 Farma tribesmen. El Kamin, a nearby oasis, has a population of 32 Bedouin tribesmen and 8 Farima tribesmen. A lost soldier (from another country), accidentally seperated from his army unit, is wandering through the desert and arrives at the edge of one of the oases. The soldier has no idea which oasis he has found, but the first person he spots from a distance is a Bedouin. What is the probability that he wandered into Abu Illan?

A. 7/20
B. 5/13
C. 1/2
D. 8/13
E. 13/20

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Re: The oasis output of Abu Ilan in the heart of the Negev desert, has a [#permalink] New post  28 Jan 2021, 06:45
Probability of finding Bedouin in Abu Ilan = 20/40 = 1/2

Probability of finding Bedouin in El Kamin = 32/40 = 4/5

Given Bedouin, probability of Abu Ilan = 1/2/(1/2+4/5) = 5/13

Option B

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Re: The oasis output of Abu Ilan in the heart of the Negev desert, has a [#permalink] New post  08 Feb 2021, 11:15
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Bunuel wrote:
The oasis output of Abu Ilan in the heart of the Negev desert, has a population of 20 Bedouin tribesmen and 20 Farma tribesmen. El Kamin, a nearby oasis, has a population of 32 Bedouin tribesmen and 8 Farima tribesmen. A lost soldier (from another country), accidentally seperated from his army unit, is wandering through the desert and arrives at the edge of one of the oases. The soldier has no idea which oasis he has found, but the first person he spots from a distance is a Bedouin. What is the probability that he wandered into Abu Illan?

A. 7/20
B. 5/13
C. 1/2
D. 8/13
E. 13/20

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Solution:

P(Bedouin) = P(Bedouin from Abu Ilan) * P(Abu Ilan) + P(Bedouin from El Kamin) * P(El Kamin)

= 20/40 * 1/2 + 32/40 * 1/2

= 10/40 + 16/40 = 26/40 = 13/20

P(Abu Ilan given Bedouin) = P(Bedouin from Abu Ilan) * P(Abu Ilan) / P(Bedouin)

= (10/40) / (13/20) = 1/4 x 20/13 = 5/13

Answer: B
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