Step-by-step explanation:
I am not sure I understand what we need to do here.
if I take this literally, then this is a table that you need to fill with the results of the experiments (how many marbles of what color were picked).
so, there would be nothing to calculate, just to do the experiments and document the results. the table would have different numbers for everybody. like when rolling some dice and recording the results.
therefore, there would be no right or wrong answer.
if you think there is a right answer, then this is a different type of question or request, which is NOT described here.
I could imagine that the question is how many marbles of what color do we EXPECT to see in the experiments of 12 and 8 pulled balls. THIS is something we CAN calculate, and where there is a right answer.
so, is that the request here ?
just in case I will give you the answer to that assumed question :
if I understand the given information correctly, then in total we have 28+14+7+35 = 84 marbles.
28 of them are orange, 14 purple, 7 black and 35 white.
that means the fraction of marbles representing orange is
28/84 = 1/3
the fraction of marbles representing purple is
14/84 = 1/6
the fraction of marbles representing black is
7/84 = 1/12
and the fraction of marbles representing white is
35/84 = 5/12
as the expected result per color in the experiments we would expect to see the same ratio (the same structure of fractions) as with the total numbers. similar to rolling a die and expecting to see each number to appear the same amount of times.
that means, when pulling 12 marbles randomly, we would expect to get
1/3 × 12 = 4 orange marbles
1/6 × 12 = 2 purple marbles
1/12 × 12 = 1 black marble
5/12 × 12 = 5 white marbles
now, when pulling only 8 marbles, what do we expect to get ?
1/3 × 8 = 8/3 marbles ≈ (rounded) 3 orange marbles
1/6 × 8 = 8/6 = 4/3 marbles ≈ 1 purple marble
1/12 × 8 = 8/12 = 2/3 ≈ 1 black marble
5/12 × 8 = 40/12 = 10/3 ≈ 3 white marbles
