Final answer:
The probability of selecting a black marble from a bag with various colored marbles is the number of black marbles divided by the total number of marbles, which is 2/11. The given options do not include the correct answer.
Step-by-step explanation:
The question is about finding the probability of selecting a black marble from a bag containing various colored marbles. To calculate this probability, we need to know the total number of marbles and the number of black marbles. In this case, we have a total of 12 red marbles, 4 black marbles, 4 purple marbles, and 2 pink marbles, which sums up to 22 marbles (12 + 4 + 4 + 2 = 22).
The number of favourable outcomes for selecting a black marble is the number of black marbles, which is 4. The probability of selecting a black marble is therefore the number of black marbles divided by the total number of marbles. This gives us a probability of 4/22, which simplifies to 2/11. None of the provided options (1/6, 1/5, 1/4, 1/3) are correct.