Final answer:
The probability of drawing 1 black and then 1 white marble in sequence from a jar containing 8 black and 4 white marbles, without replacement, is 8/33.
Step-by-step explanation:
To calculate the probability of drawing 1 black and then 1 white marble from a jar that contains 8 black marbles and 4 white marbles, without replacement, we will evaluate two separate events: first drawing a black marble, and then drawing a white marble. There are 12 marbles in total (8 black + 4 white).
For the first event, the probability of drawing a black marble is 8/12 or simplified to 2/3. After drawing a black marble, there are now 7 black and 4 white marbles left, making a total of 11 marbles. Therefore, the probability of drawing a white marble on the second draw is 4/11. To find the overall probability of both events happening in sequence, we multiply the two individual probabilities together:
The probability of drawing 1 black then 1 white marble = (Probability of black on the first draw) × (Probability of white on a second draw) = 2/3 x 4/11 = 8/33.
Thus, the probability of drawing 1 black and then 1 white marble in this manner is 8/33.