Question

A die is rolled four times and the numbers appearing on each roll are noted.

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

For probability problems, always compare the possible outcomes to the total number of possible outcomes to find the correct probability.

Answer 1

The Correct Option is A

We are asked to compare the probability that the four numbers rolled on a die are distinct and in ascending order with the given value 518518. Step 1: Calculate the probability.
When rolling a die four times, the total number of possible outcomes is: \[ 6^4 = 1296 \] Now, for the numbers to be distinct and in ascending order, we need to choose 4 distinct numbers from the 6 available options and arrange them in one specific way (ascending order). The number of ways to select 4 distinct numbers from 6 is: \[ \binom{6}{4} = \frac{6 \times 5}{2 \times 1} = 15 \] Since the numbers must be in ascending order, there is only 1 way to arrange each selection. Therefore, the probability is: \[ P(\text{distinct and in ascending order}) = \frac{15}{1296} = \frac{5}{432} \]
Step 2: Compare with Quantity B.
Given that Quantity B is 518518, which is much greater than \( \frac{5}{432} \), we can conclude that Quantity A is smaller than Quantity B.
Final Answer: \[ \boxed{\text{Quantity B is greater.}} \]