Final answer:
When a fair six-sided die is rolled, each side from 1 to 6 has an equal chance of facing up, so the probability of landing on 1 is the same as landing on 6, and the correct answer is b. the probabilities are equal.
Step-by-step explanation:
The question pertains to the properties of probability in a scenario where a fair six-sided die is involved. When a fair six-sided die is rolled, each of the six faces (labeled with numbers 1 through 6) has an equal chance of landing face up. This means the probabilities are equal for each number. In the context of the original question, the probability of landing on 1 is the same as the probability of landing on 6 because both are outcomes on a fair die. Therefore, the correct answer is b. the probabilities are equal.
If you roll the die one time, there would be six possible outcomes, each with an equal chance of occurring, which is 1/6. If you flip a coin and combine that with rolling a die, you double the number of possible outcomes, because each die result could come with either a Head (H) or a Tail (T), resulting in 12 possible outcomes (e.g., H1, T1, H2, T2, ..., H6, T6). Neither the roll of the die nor the flip of the coin affects the other, illustrating the concept of independent events. Each combination has a probability of 1/12 when a fair coin and a fair die are used consecutively.