Bowls A and B contain a number of white and red balls. Clark repeatedly selected a ball from both bowls and recorded the results in a table. If there are 500 balls in Bowl B, what is the estimated difference in the expected number of white and red balls in Bowl B?
Bowl A : 45, 55
Bowl B : 60, 40
Number of white balls selected : 45, 60
Number of red balls selected : 55, 40
To find the estimated difference in the expected number of white and red balls in Bowl B, we need to calculate the expected numbers of white and red balls in Bowl B.
First, let's calculate the expected number of white balls in Bowl B:
- In Bowl B, the ratio of white balls to total balls is 60/100 = 0.6.
- Since Bowl B contains 500 balls, the expected number of white balls in Bowl B is 0.6 * 500 = 300.
Next, let's calculate the expected number of red balls in Bowl B:
- In Bowl B, the ratio of red balls to total balls is 40/100 = 0.4.
- Since Bowl B contains 500 balls, the expected number of red balls in Bowl B is 0.4 * 500 = 200.
Finally, we can calculate the difference between the expected number of white and red balls in Bowl B:
- The expected number of white balls in Bowl B is 300.
- The expected number of red balls in Bowl B is 200.
- The difference between these two numbers is 300 - 200 = 100.
Therefore, the estimated difference in the expected number of white and red balls in Bowl B is 100.
The expected proportion of white balls in Bowl B is simply the average of the proportion of white balls selected from Bowl B in each trial:
(60/100 + 45/100)/2 = 0.525
Similarly, the expected proportion of red balls in Bowl B is:
(40/100 + 55/100)/2 = 0.475
If there are 500 balls in Bowl B, we can estimate the number of white balls as:
0.525 x 500 = 262.5
And the number of red balls as:
0.475 x 500 = 237.5
The estimated difference in the expected number of white and red balls in Bowl B is:
262.5 - 237.5 = 25
Therefore, the estimated difference in the expected number of white and red balls in Bowl B is 25.
To find the estimated difference in the expected number of white and red balls in Bowl B, we need to calculate the expected number of white and red balls separately and then find the difference.
For Bowl B, we are given the numbers of white balls (60) and red balls (40) that were selected.
To find the expected number of white balls in Bowl B, we can use the proportion of white balls selected from Bowl B to the total number of balls selected from both bowls:
Expected number of white balls in Bowl B = (Number of white balls selected from Bowl B / Total number of balls selected) * Total number of balls in Bowl B
Expected number of white balls in Bowl B = (60 / (60 + 45)) * 500
Expected number of white balls in Bowl B = (60 / 105) * 500
Expected number of white balls in Bowl B ≈ 285.714
Similarly, to find the expected number of red balls in Bowl B, we can use the proportion of red balls selected from Bowl B to the total number of balls selected:
Expected number of red balls in Bowl B = (Number of red balls selected from Bowl B / Total number of balls selected) * Total number of balls in Bowl B
Expected number of red balls in Bowl B = (40 / (40 + 55)) * 500
Expected number of red balls in Bowl B = (40 / 95) * 500
Expected number of red balls in Bowl B ≈ 210.526
Finally, we can calculate the estimated difference in the expected number of white and red balls in Bowl B:
Estimated difference = Expected number of white balls in Bowl B - Expected number of red balls in Bowl B
Estimated difference = 285.714 - 210.526
Estimated difference ≈ 75.188
Therefore, the estimated difference in the expected number of white and red balls in Bowl B is approximately 75.188.