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:

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" |

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

#### Video Explanation

Scroll down for explanatory answer text#### Explanatory Answer

#### Use these hints to get the answer

- Compute the number of ways the letters of the word 'Math' can be reordered.
- Compute the probability of getting the word 'Math'.
- Compute the number of ways the letters of the word 'Good' can be reordered.
- Compute the probability of getting the word 'Good'.

#### 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})

#### 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' repeat.

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})

#### 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 answer.