Final answer:
The probability of first picking a red marble and then a black marble without replacement is calculated by multiplying the individual probabilities of each event. The correct answer is C. 0.16.
Step-by-step explanation:
The question involves calculating the probability of two dependent events: picking a red marble followed by a black marble without replacement from a pouch containing variously colored marbles.
To find the probability of two dependent events, you multiply the probability of the first event by the probability of the second event, given that the first event has occurred. The pouch originally contains 8 black marbles, 5 white marbles, and 12 red marbles, totaling 25 marbles altogether.
First, we determine the probability of picking a red marble. There are 12 red marbles out of the total 25, so the probability is 12/25. After picking a red marble and not replacing it, there are now 24 marbles left in the pouch, 8 of which are black. Thus, the probability of then picking a black marble is 8/24 or 1/3 when rounded down.
Multiplying these probabilities gives us the overall probability of picking a red marble first and then a black marble: (12/25) × (1/3) = 12/75, which simplifies to 4/25. Converting this to a decimal gives us 0.16.
Therefore, the correct answer is C. 0.16.