Number of White Balls Selected Number of Red Balls Selected
Bowl A 45 55
Bowl B 60 40
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?Number of White Balls Selected Number of Red Balls Selected
Bowl A 45 55
Bowl B 60 40
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?
First, we need to find the proportion of white and red balls in each bowl based on the selections made by Clark.
For Bowl A:
- Proportion of white balls = 45/100 = 0.45
- Proportion of red balls = 55/100 = 0.55
For Bowl B:
- Proportion of white balls = 60/100 = 0.6
- Proportion of red balls = 40/100 = 0.4
Next, we need to estimate the expected number of white and red balls in Bowl B based on these proportions, since we know there are 500 balls in Bowl B.
Expected number of white balls in Bowl B = 0.6 x 500 = 300
Expected number of red balls in Bowl B = 0.4 x 500 = 200
The estimated difference in the expected number of white and red balls in Bowl B is:
300 - 200 = 100
Therefore, the estimated difference is 100.
To find the estimated difference in the expected number of white and red balls in Bowl B, we need to calculate the average difference for each ball selection between Bowl B and Bowl A.
First, let's find the average number of white balls selected and red balls selected for each bowl:
- Bowl A:
- Average number of white balls selected = 45
- Average number of red balls selected = 55
- Bowl B:
- Average number of white balls selected = 60
- Average number of red balls selected = 40
Next, let's calculate the difference in the expected number of white balls and red balls for each selection:
- Difference in expected number of white balls = Average number of white balls selected in Bowl B - Average number of white balls selected in Bowl A
= 60 - 45
= 15
- Difference in expected number of red balls = Average number of red balls selected in Bowl B - Average number of red balls selected in Bowl A
= 40 - 55
= -15
Finally, the estimated difference in the expected number of white and red balls in Bowl B is the sum of the two differences:
- Estimated difference = Difference in expected number of white balls + Difference in expected number of red balls
= 15 + (-15)
= 0
Therefore, the estimated difference in the expected number of white and red balls in Bowl B is 0.
To find the estimated difference in the expected number of white and red balls in Bowl B, we will use the information provided in the table.
First, let's calculate the proportion of white and red balls selected from each bowl.
For Bowl A:
- Number of white balls selected: 45
- Number of red balls selected: 55
- Total number of balls selected: 45 + 55 = 100
Proportion of white balls selected from Bowl A: 45/100 = 0.45
Proportion of red balls selected from Bowl A: 55/100 = 0.55
For Bowl B:
- Number of white balls selected: 60
- Number of red balls selected: 40
- Total number of balls selected: 60 + 40 = 100
Proportion of white balls selected from Bowl B: 60/100 = 0.6
Proportion of red balls selected from Bowl B: 40/100 = 0.4
Now, let's estimate the expected number of white and red balls in Bowl B based on these proportions and the total number of balls in Bowl B (which is given as 500).
Expected number of white balls in Bowl B: Proportion of white balls selected from Bowl B * Total number of balls in Bowl B = 0.6 * 500 = 300
Expected number of red balls in Bowl B: Proportion of red balls selected from Bowl B * Total number of balls in Bowl B = 0.4 * 500 = 200
The estimated difference in the expected number of white and red balls in Bowl B is calculated by subtracting the expected number of red balls from the expected number of white balls:
Estimated difference = Expected number of white balls - Expected number of red balls = 300 - 200 = 100
Therefore, the estimated difference in the expected number of white and red balls in Bowl B is 100.