Final answer:
The probability of drawing 2 black marbles from a bag with 45 black and 25 white marbles is calculated by multiplying the probability of drawing one black marble and then another without replacement, resulting in a probability of 33/161, which does not match the provided options.
Step-by-step explanation:
The student is asking about the probability of drawing 2 black marbles from a bag that contains a total of 45 black marbles and 25 white marbles. To find this probability, we will perform two steps: calculate the probability of drawing the first black marble and then calculate the probability of drawing a second black marble, given that the first marble drawn was black and is not replaced.
The probability of drawing the first black marble is 45 out of the total number of marbles (45 black + 25 white), which is 70. So, the probability is 45/70. After drawing one black marble, there are 44 black marbles left and still a total of 69 marbles in the bag. The probability of drawing a second black marble is then 44/69.
To find the combined probability of both events happening in succession, we multiply the two probabilities: (45/70) × (44/69). Simplifying the fraction gives us the probability of drawing 2 black marbles without replacement as:
(45/70) × (44/69) = (9/14) × (22/69) = 198/966 = 33/161
This probability does not match any of the provided options (A-D), indicating a possible mistake in the question or the answer choices.