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A doctor claims that 60% of the patients he examines are all

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A doctor claims that 60% of the patients he examines are all [#permalink]

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New post 27 Dec 2012, 11:47
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A doctor claims that 60% of the patients he examines are allergic to some type of weeds. What is the probability that exactly three of the next 4 patient he examines are allergic to weeds?

It'll be great if problem is solved step by step with explanation.

Kudos [?]: 5 [0], given: 1

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Re: A doctor claims that 60% of the patients he examines are all [#permalink]

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New post 27 Dec 2012, 23:29
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mihir66 wrote:
A doctor claims that 60% of the patients he examines are allergic to some type of weeds. What is the probability that exactly three of the next 4 patient he examines are allergic to weeds?

It'll be great if problem is solved step by step with explanation.


The probability of a person being allergic = 6/10
Probability of a person not being allergic = 4/10

Probability of first person being allergic = 6/10
Probability of second person being allergic = 6/10
Probability of third person being allergic = 6/10
Probability of fourth person not being allergic = 4/10

Probability that exactly 3 of the next 4 people are allergic = (6/10)*(6/10)*(6/10)*(4/10)*4
We multiply by 4 because the non allergic person could be first, second or third. So we need to account for all sequences AAAN, AANA, ANAA, NAAA
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Kudos [?]: 17827 [2], given: 235

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Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 742 [0], given: 355

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Re: A doctor claims that 60% of the patients he examines are all [#permalink]

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New post 12 May 2014, 07:45
I would guess this question is just (4)(3^3)(2) / (5^3)(5)=216/625

Therefore answer is A (J/K, would be nice to have some answer choices!)

Cheers!
J :)

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Re: A doctor claims that 60% of the patients he examines are all [#permalink]

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New post 06 Oct 2016, 16:10
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Kudos [?]: 283 [0], given: 0

Re: A doctor claims that 60% of the patients he examines are all   [#permalink] 06 Oct 2016, 16:10
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