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01 Oct 2024, 10:28
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
66% (02:48) correct
33% (01:21) wrong based on 3 sessions
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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?
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22 Feb 2025, 23:09
Kudos
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OE
In the context of this problem, (n r) represents the number of ways r specimens can be selected without replacement from n specimens.
The probability that only 1 of the 5 specimens selected from the 40 specimens will have the trait is equal to
number of ways to select 5 specimens, only 1 of which has the trait/number of ways to select 5 specimens.
The number of ways 5 specimens can be selected from the 40 specimens is (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 (1 3) (37 4). So the probability that only 1 of the 5 specimens selected will have the trait is represented by (3 1)(37 4 ) (40 5). The correct answer is Choice E.
Answer: E
In the context of this problem, (n r) represents the number of ways r specimens can be selected without replacement from n specimens.
The probability that only 1 of the 5 specimens selected from the 40 specimens will have the trait is equal to
number of ways to select 5 specimens, only 1 of which has the trait/number of ways to select 5 specimens.
The number of ways 5 specimens can be selected from the 40 specimens is (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 (1 3) (37 4). So the probability that only 1 of the 5 specimens selected will have the trait is represented by (3 1)(37 4 ) (40 5). The correct answer is Choice E.
Answer: E
