To estimate the number of white balls in Bowl A based on Simon's results, we first need to analyze the data provided.
From the table, we have:
- In Bowl A, Simon selected 5 white balls and 15 red balls.
- In Bowl B, Simon selected 16 white balls and 4 red balls.
Now, we can find the total number of balls selected from both bowls:
Bowl A:
- Total balls selected = 5 (white) + 15 (red) = 20 balls
Bowl B:
- Total balls selected = 16 (white) + 4 (red) = 20 balls
Now we can calculate the proportion of white and red balls selected from both bowls.
Bowl A:
- Proportion of white balls = Number of white balls selected from A / Total balls selected from A = 5 / 20 = 0.25
Bowl B:
- Proportion of white balls = Number of white balls selected from B / Total balls selected from B = 16 / 20 = 0.8
Now, let's find the weighted average proportion of white balls based on the total selections from both bowls:
Total white balls selected = 5 (from A) + 16 (from B) = 21
Total balls selected = 20 (from A) + 20 (from B) = 40
Weighted proportion of white balls = Total white balls selected / Total balls selected = 21 / 40 = 0.525
Now, if there are 36 balls in Bowl A, we can estimate the number of white balls in Bowl A by multiplying the total number of balls by the proportion of white balls.
Estimated number of white balls in Bowl A = 36 * (proportion of white balls in A)
Since we only focused on Bowl A's selection and want to estimate its composition, we use the proportion of white balls just from Bowl A.
Thus, we get:
Estimated white balls in Bowl A = 36 * (5/20) = 36 * 0.25 = 9.
So the estimated number of white balls in Bowl A is 9.