Final answer:
Sophia will draw a purple marble approximately 120 times.
Step-by-step explanation:
Sophia will draw a purple marble approximately 120 times.
To find the probability of drawing a purple marble, we need to calculate the probability of drawing a purple marble on each individual draw and then multiply it by the total number of draws. The probability of drawing a purple marble on each draw is 3/7 (3 purple marbles out of 7 total).
So, the probability of drawing a purple marble on each of the 280 draws is (3/7) * 280 = 120 purple marbles.