Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A bag contains black, white, gray, red, and blue marbles. Each of the 20 students in class is asked to reach in the bag and choose a marble. The color is recorded and the marble is replaced in the bag before the next draw. The results are shown below.





Marbles
Number of Draws


Black
4


White
7


Gray
2


Red
6


Blue
1




Based on these results, what is the best prediction of the number of black or red marbles in the bag if it contains 80 marbles?

2121. A bag contains black, white, gray, red, and blue marbles. Each of the 2020 students in class is asked to reach in the bag and choose a marble. The color is recorded and the marble is replaced in the bag before the next draw. The results are shown below.\newline\begin{tabular}{|c|c|}\newline\hline Marbles & Number of Draws \\\newline\hline Black & 44 \\\newline\hline White & 77 \\\newline\hline Gray & 22 \\\newline\hline Red & 66 \\\newline\hline Blue & 11 \\\newline\hline\newline\end{tabular}\newlineBased on these results, what is the best prediction of the number of black or red marbles in the bag if it contains 8080 marbles?

Full solution

Q. 2121. A bag contains black, white, gray, red, and blue marbles. Each of the 2020 students in class is asked to reach in the bag and choose a marble. The color is recorded and the marble is replaced in the bag before the next draw. The results are shown below.\newline\begin{tabular}{|c|c|}\newline\hline Marbles & Number of Draws \\\newline\hline Black & 44 \\\newline\hline White & 77 \\\newline\hline Gray & 22 \\\newline\hline Red & 66 \\\newline\hline Blue & 11 \\\newline\hline\newline\end{tabular}\newlineBased on these results, what is the best prediction of the number of black or red marbles in the bag if it contains 8080 marbles?
  1. Total draws calculation: Total draws: 44 (Black) + 77 (White) + 22 (Gray) + 66 (Red) + 11 (Blue) = 2020 draws.
  2. Black and Red draws: Black and Red draws combined: 44 (Black) + 66 (Red) = 1010 draws.
  3. Proportion calculation: Proportion of Black and Red draws to total draws: 1020=12\frac{10}{20} = \frac{1}{2}.
  4. Total Black and Red marbles: If there are 8080 marbles in total, and Black and Red marbles are half based on the draw proportion, then: 80×(12)=4080 \times (\frac{1}{2}) = 40 marbles.

More problems from Estimate population size using proportions