Final answer:
The probability of rolling at least one 3 in 8 rolls of a standard dice is 1 - (5/6)^8. This is calculated by subtracting the probability of not rolling a 3 in any of the rolls from 1.
Step-by-step explanation:
The student is asking for the probability of rolling at least one 3 in the next 8 rolls of a standard six-sided dice. To find this probability, we need to consider the opposite event, which is not rolling a 3 in any of the 8 rolls. The probability of not rolling a 3 on any given roll is 5/6. To find the probability for 8 rolls, we raise this to the 8th power, which gives us (5/6)^8. However, since we are interested in the probability of rolling at least one 3, we subtract this probability from 1, getting our answer as 1 - (5/6)^8, which corresponds to the option a in the question provided.