A bag contains 100 marbles, some red and some purple. Suppose a student, without looking, chooses a marble out of the bag, records the color, and then places that marble back in the bag. The student has recorded 9 red marbles and 11 purple marbles. Using these results, predict the number of red marbles in the bag.
9 of the 20 drawn were red
9/20 * 100 = 45
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Well, it seems like this student has really been keeping a close eye on those marbles. They've recorded 9 red marbles and 11 purple marbles. Now, in order to predict the number of red marbles in the bag, we need to tap into our inner mathematician. It's time to do some sleuthing!
Since the student is placing the marble back in the bag after recording its color, we can assume that each time they pick a marble, it's like starting with a fresh set of 100 marbles. Therefore, the probability of picking a red marble is consistent throughout.
The student has recorded 9 red marbles. So, if we assume they've picked marbles randomly (as randomly as a student can be), we can say that the proportion of red marbles in the bag is approximately 9/20.
Now, if we let "x" represent the number of red marbles in the bag, we can set up the following proportion:
x/100 ≈ 9/20
And, through the magic of cross-multiplication, we get:
20x ≈ 900
Solving for x, we divide both sides of the equation by 20, giving us:
x ≈ 45
Therefore, our prediction is that there are about 45 red marbles in the bag. But keep in mind, this is just an approximation based on the limited data provided by our vigilant student. So, take it with a grain of marble!
To predict the number of red marbles in the bag, we can make use of probability.
Since the student recorded 9 red marbles and 11 purple marbles, we can consider this as a sample of 20 marbles being drawn (9 red + 11 purple).
The probability of drawing a red marble from the bag is given by the ratio of the number of red marbles to the total number of marbles in the bag. Let's assume the number of red marbles in the bag is denoted by "x".
The probability of drawing a red marble from the bag can be calculated as:
P(red) = 9/20
And the ratio of the number of red marbles to the total number of marbles in the bag is:
x/100 = 9/20
To solve for "x" (the number of red marbles in the bag), we can cross-multiply and solve for "x":
20x = 9 * 100
20x = 900
x = 900/20
x = 45
Therefore, we can predict that there are 45 red marbles in the bag.
To predict the number of red marbles in the bag, we can use the concept of probability. Let's assume that the proportion of red marbles in the bag is the same as the proportion observed by the student.
The student recorded 9 red marbles out of a total of 20 marbles drawn (9 red + 11 purple). So, the probability of drawing a red marble is 9/20.
Now, if we assume that the same probability applies to the entire bag, we can set up a proportion to find the number of red marbles in the bag:
(9 red marbles / 20 marbles) = (x red marbles / 100 marbles)
To solve for x (the number of red marbles in the bag), we can cross multiply:
9/20 * 100 = x
9/20 * 100 = 45
Therefore, based on the results recorded by the student, we can predict that there are 45 red marbles in the bag.