Final answer:
The probability of drawing two red marbles from the jar without replacement is 1/205, which is calculated by multiplying the probabilities of drawing a red marble in successive draws. This does not match any of the provided multiple-choice answers, indicating a possible error in the provided options or the question setup.
Step-by-step explanation:
The student's question asks for the probability of pulling two red marbles from a jar containing 8 red marbles and 33 blue marbles, without replacement. To find this probability, we use the formula for combinatorial probability as the draws are dependent events. First, we find the probability of drawing one red marble, which is ⅓ (8 out of 41 total marbles). Without replacing that marble, the jar now has 7 red marbles and 33 blue marbles (40 in total), so the probability of drawing another red marble is ⅗.
We then multiply these two probabilities to get the probability of both events happening in succession: (⅓) × (⅗) = (⅔) × (⅗) = 8/1640 = 1/205. This result is not listed in the multiple-choice options provided, so we may need to verify if there was an error in the given options or in the initial setup of the question.
If we compare this solution to the given options: a) 2/455, b) 16/455, c) 33/455, d) 8/67, none of these match our calculated probability of 1/205. The correct step-by-step method for calculating such probability was demonstrated, which is critical for understanding combinatorial probability in finite discrete sample spaces.