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?
To find the estimated difference in the expected number of white and red balls in Bowl B, we first need to determine the proportion of white and red balls in Bowl B.
Let's say the proportion of white balls in Bowl B is \( p_w \) and the proportion of red balls in Bowl B is \( p_r \).
From the information given, we know that Clark repeatedly selected a ball from both bowls. This means that the expected proportion of white balls selected from Bowl B should be equal to the expected proportion of white balls in the entire bowl.
Therefore, we can set up the following equation:
\( p_w = \dfrac{W}{500} \)
where \( W \) is the estimated number of white balls in Bowl B.
Given that the expected proportion of red balls selected from Bowl B should also be equal to the expected proportion of red balls in the entire bowl, we can set up a similar equation for red balls:
\( p_r = \dfrac{R}{500} \)
where \( R \) is the estimated number of red balls in Bowl B.
We can then find the estimated difference in the expected number of white and red balls in Bowl B by subtracting the estimated number of red balls from the estimated number of white balls:
\( W - R \)