The order of events from the highest to lowest probability is as follows:
The difference of the two numbers is at most 1 (11/36).
The second number is a multiple of the first number (7/36).
Getting the same number on each roll (1/6).
Obtaining an odd prime number on each roll (1/36).
Certainly, let's delve into a more detailed explanation of the probabilities:
The probability of obtaining an odd prime number (excluding 1) on each roll:
A six-sided die has odd prime numbers 3 and 5. Each of these has a probability of 1/6. The probability of obtaining an odd prime number on each roll is calculated by multiplying the individual probabilities, resulting in 1/36.
The probability of getting the same number on each roll:
Since there are six possible outcomes (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) out of 36 total outcomes, the probability of getting the same number on each roll is 6/36, which simplifies to 1/6.
The probability that the difference of the two numbers is at most 1:
Considering the pairs (1,1), (2,1), (2,2), (3,2), (3,3), (4,3), (4,4), (5,4), (5,5), (6,5), (6,6), there are 11 favorable outcomes out of 36 possible outcomes, resulting in a probability of 11/36.
The probability that the second number is a multiple of the first number:
Examining the pairs (2,1), (3,1), (4,1), (4,2), (5,1), (5,5), (6,1), there are 7 favorable outcomes out of 36, leading to a probability of 7/36.