As seen from the table below, out of the thirty-six equally probable rolls, eighteen result in the same color facing upward on both dice (indicated by an "S"); eighteen result in different colors facing upward (indicated by a "D").

The events occur with the same frequency, so they also occur with the same probability.

As seen from the table below, out of the thirty-six equally probable rolls, twenty result in an even sum (these are set apart with red squares), and sixteen result in an odd sum.

Since even sums happen with greater frequency, the probability of an even sum is greater.

The diagram below shows how the balls are separated. 

Box A contains 13 balls, of which 4 are white; the probability of a random draw from this box resulting in the draw of a white ball is . 

Box B contains 12 balls, of which 6 are white;  the probability of a random draw from this box resulting in the draw of a white ball is .

Rewriting the probabilities in terms of a common denominator:

, so , making the draw of a white ball more likely from Box B.

The rolls that yield a product greater than or equal to 20 are:

These are 8 out of 36 rolls, so the probability of getting one of them is 

The gray region is the region outside both  and  and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3:  and . 

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as . Therefore, it is the correct choice.

The gray region is the region outside both  and  and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3:  and . 

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as . Therefore, it is the correct choice.

The midrange of a data set is the mean of its least and greatest elements. The midrange of the first data set is ; that of the second data set is . (A) is greater.

To find the range of a set of numbers, you do not even have to put them in order.  You merely need to subtract the smallest value from the largest.  Given the way of constructing set  by doubling set 's values, the largest and smallest values in  will directly correlate to the same in set :

Smallest:  

Largest: 

Therefore, the range  is: 

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way that we construct set  from the function , we merely need to use that function to find the smallest and largest values. Luckily, that is pretty easy for this question. The smallest will be  and the largest will be 

Smallest:  

Largest: 

Therefore, the range  is: 

We first need to determine the members of set . Using our function, we will get:

Our largest value is , and our smallest value is ; therefore, the range is