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09 Dec 2018, 00:53
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Difficulty:
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22%
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A certain fish tank holds a total of 42 fish among four compartments. If the numbers of fish in the compartments are consecutive, what is the probability that a given fish is in the compartment that holds the most fish?
(A) \(\frac{11}{42}\)
(B) \(\frac{5}{21}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{3}{14}\)
(E) \(\frac{2}{7}\)
(A) \(\frac{11}{42}\)
(B) \(\frac{5}{21}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{3}{14}\)
(E) \(\frac{2}{7}\)
eabhgoy
Joined: 12 Apr 2011
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Concentration: Strategy, Marketing
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09 Dec 2018, 02:20
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Total number of fishes = 42
Number of compartments = 4
Average number of fishes per compartment = 42/4 = 10.5
Hence the consecutive numbers will be on both sides of 10.5 i.e. 9,10,11,12
The compartment with the maximum number of fishes = 12
Probability = 12/42 = 2/7
Hence the correct answer is E
Posted from my mobile device
Number of compartments = 4
Average number of fishes per compartment = 42/4 = 10.5
Hence the consecutive numbers will be on both sides of 10.5 i.e. 9,10,11,12
The compartment with the maximum number of fishes = 12
Probability = 12/42 = 2/7
Hence the correct answer is E
Posted from my mobile device
04 Sep 2019, 11:13
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For consecutive integer problems I let x= the first integer, then (x+1)= the second integer and so on.
In this problem, 4 consecutive integers add up to 42, therefore:
x+(x+1)+(x+2)+(x+3)=42
4x+6=42
4x=36
x=9
The first integer is 9, the second must be 10, the third must be 11, the fourth must be 12.
The probability that a given fish is from the compartment that holds the most fish can be expressed as:
(the number of fish in the compartment with the most fish=12)/(total number of fish=42)
this reduces to 2/7
The correct answer is answer choice E.
Please give kudos if this was helpful in any way!
In this problem, 4 consecutive integers add up to 42, therefore:
x+(x+1)+(x+2)+(x+3)=42
4x+6=42
4x=36
x=9
The first integer is 9, the second must be 10, the third must be 11, the fourth must be 12.
The probability that a given fish is from the compartment that holds the most fish can be expressed as:
(the number of fish in the compartment with the most fish=12)/(total number of fish=42)
this reduces to 2/7
The correct answer is answer choice E.
Please give kudos if this was helpful in any way!
