GRE® Quant Practice | Probability Q4

Reordering of n objects | GRE Quantitative Comparison

This GRE quant practice question is a quantitative comparison question. Comparing probabilities of two events and identifying which between the two has a larger probability. Concept tested: number of ways of reordering elements when all are distinct and when not all are same.

Question 4: Quantitative Comparison

Quantity A Quantity B
The probability that a word selected from the set of all rearrangements of the letters of the word "Math" results in "Math" The probability that a word selected from the set of all rearrangements of the letters of the word "Good" results in "Good"

  1. Quantity A is greater
  2. Quantity B is greater
  3. The two quantities are equal
  4. The relationship cannot be determined from the information given

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Explanatory Answer | GRE Probability Questionbank Question 4

Step 1 of solving this GRE Comparison Question: Evaluate Quantity A

Compute the number of ways the letters of the word 'Math' can be reordered.

All 4 letters of the word 'Math' are distinct.
The letters of the word 'Math' can therefore, be reordered in 4! ways = 24 ways.

Compute the required probability

Of the 24 different word orders, only one will be 'Math'.
Therefore, the probability that a word selected out of the 24 turns out to be 'Math' is \\frac{1}{24})


Step 2 of solving this GRE Comparison Question: Evaluate Quantity B

Compute the number of ways the letters of the word 'Good' can be reordered.

Two of the 4 letters of the word 'Good' are the same. O appears twice.
The letters of the word 'Good' can therefore, be reordered in \\frac{4!}{2!}) = 12 ways.

Compute the required probability

Of the 12 different word orders, only one will be 'Good'.
Therefore, the probability that a word selected out of the 12 turns out to be 'Good' is \\frac{1}{12})


Step 3 of solving this GRE Comparison Question: The Comparison

Quantity A value = \\frac{1}{24}) Quantity B value = \\frac{1}{12})
Between fractions having the same numerator, the one with the smaller denominator is the larger fraction.
Fraction in quantity B is 1 out 12 parts - while the fraction in quantity A is 1 out of 24 parts - so quantity A is smaller.
Quantity B is greater.

Choice B is the correct answer



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