Final answer:
The probability of rolling a pair of identical numbers with a fair six-sided die in two rolls is 1/6, or approximately 16.67%.
Step-by-step explanation:
The student is asking about the probability of rolling a pair of identical numbers on a fair six-sided die in two rolls.
This probability question relates to the concept of independent events in probability theory. When you roll a die, each of the six faces (numbered 1 through 6) has an equal chance of landing face up.
Since the events are independent, the outcome of the first roll does not affect the outcome of the second roll.
For the first roll, any number can come up, so there are 6 possible outcomes.
On the second roll, in order to match the first roll, there is only 1 favorable outcome (the same number that came up on the first roll).
Therefore, the probability of rolling the same number on the second roll as the first is 1 in 6, or 1/6.
Thus, the probability of achieving a pair of identical numbers in just two rolls of a fair six-sided die is 1/6 or approximately 16.67%.
Question: 20.3 program 2a: In a thrilling game of chance, you're rolling a fair six-sided die, hoping for a pair of identical numbers. What is the probability of achieving this exhilarating outcome in just two rolls?