A bag contains 45 marbles of various colors. Jon draws 60 times, each time replacing the marble before drawing again. He gets a total of 12 blue marbles.
Which is best prediction of how many blue marbles are in the bag?
12/60 = 1/5
(1/5) * 45 = ?
To predict the number of blue marbles in the bag, we can use the concept of probability. Since Jon drew 60 times with replacement and got 12 blue marbles, we can assume that the probability of drawing a blue marble on each draw is constant.
To calculate the best prediction, we can use the ratio of the number of blue marbles Jon drew to the total number of draws he made. In this case, the ratio is 12 blue marbles out of 60 draws, which simplifies to 1 blue marble out of every 5 draws.
To estimate the number of blue marbles in the bag, we can assume that the same probability applies to the entire bag. If Jon drew 12 blue marbles out of 60 draws, then we can predict that there are approximately 12 blue marbles for every 60 marbles in the bag.
To find the best prediction of how many blue marbles are in the entire bag, we need to determine the proportion of blue marbles in relation to the total number of marbles. Since the ratio is 1 blue marble out of every 5 draws, we can create a proportion equation:
1 blue marble / 5 draws = x blue marbles / 45 total marbles
To solve for x, we can cross-multiply and divide:
x = (1 blue marble / 5 draws) * 45 total marbles
x = 9 blue marbles
Therefore, the best prediction for the number of blue marbles in the bag is approximately 9.