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QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci

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QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink] New post 12 Sep 2016, 01:29
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Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If 5 specimens are to be selected from the dish at random and without replacement, which of the following represents the probability that only 1 of the 5 specimens selected will have the trait?

A) \(\frac{\frac{5}{1}}{\frac{40}{3}}=\)


B) \(\frac{\frac{5}{1}}{\frac{40}{5}}=\)


C) \(\frac{\frac{40}{3}}{\frac{40}{5}}=\)


D) \(\frac{\frac{3}{1} * \frac{37}{4}}{\frac{40}{3}}=\)


E)\(\frac{\frac{3}{1} * \frac{37}{4}}{\frac{40}{5}}=\)

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Question: 17
Page: 180
[Reveal] Spoiler: OA

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Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink] New post 12 Sep 2016, 01:46
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Explanation

Question like this is much better to go step by step, dividing it into chunks.

Now, we said that we have to select 1 specimens among five BUT only 3 over 40 have such traits.

To select 5 among 40 is, the total possibilities, \(\frac{40}{5}\) in the denominator

In the numerator, we have 1 specimens among 3 and then select 4 among 37 that do not have the traits.

\(\frac{3 over 1 * 37 over 4}{40 over 5}\)

The best answer is E
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Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink] New post 13 Aug 2017, 09:17
I couldn't understand the solution properly.why we take 37C4??? Is that another way to solve this math ???
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Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink] New post 13 Aug 2017, 13:13
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The probability that only 1 of the 5 specimens selected from the 40 specimens will have the trait is equal to

\(\frac{numbers of way to select 5 specimens, only 1 of which has the traits}{numbers of ways to select 5 specimens}\)

The number of ways 5 specimens can be selected from the 40 specimens is \(\frac{40}{5}\).To select 5 specimens, only 1 of which has the trait, you have to select 1 of the 3 specimens that have the trait and select 4 of the 37 specimens that do not have the trait. The number of such selections is the product \(\frac{3}{1}\) * \(\frac{37}{4}\).

So the probability that only 1 of the 5 specimens selected will have the trait is represented by \(\frac{3}{1}\) * \(\frac{37}{4}\) / \(\frac{40}{5}\)

E is the best
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Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci   [#permalink] 13 Aug 2017, 13:13
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