# 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

#### 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 #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch December 15, 2023 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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