There are 100 marbles in a bag. 200people are asked to draw a ball. Each marble drawn is put back into the bag before the next draw. 7 people draw red color marbles. How many red marbles are there in the bag?
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To determine how many red marbles are in the bag, we need to gather the given information:
- The total number of marbles in the bag is 100.
- 200 people are asked to draw a ball randomly and independently.
- Each time a ball is drawn, it is put back into the bag before the next draw.
- Out of the 200 people, 7 people draw red marbles.
From this information, we can infer that the probability of drawing a red marble remains constant throughout all the draws. Since each draw is independent, the probability of drawing a red marble for each person would be the same. Therefore, we can set up a proportion to solve for the number of red marbles in the bag.
Let's denote the number of red marbles in the bag as x. Since the probability of drawing a red marble is x/100 (x out of the total 100 marbles), we can set up the proportion:
7/200 = x/100
Now we can cross-multiply and solve for x:
7 * 100 = 200 * x
700 = 200 * x
x = 700 / 200
x = 3.5
Since we cannot have a fraction of a marble, we conclude that there are 3 red marbles in the bag.