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  3. Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If

Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If

游客2024-01-12  23
问题 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?
选项 A、 
B、 
C、 
D、 
E、 
答案 E
解析 In the context of this problem,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. 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.So the probability that only 1 of the 5 specimens selected will have the trait is represented by. The correct answer is Choice E.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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