Bowls A and B contain a number of white and red balls. Raya repeatedly selected a ball from both bowls and recorded the results in a table. If there are 500 balls in Bowl A, what is the estimated difference in the expected number of red and white balls in Bowl A?

Question

Bowls A and B contain a number of white and red balls. Raya repeatedly selected a ball from both bowls and recorded the results in a table. If there are 500 balls in Bowl A, what is the estimated difference in the expected number of red and white balls in Bowl A?
Bowl / White Marbles Selected / Red Marbles Selected
Bowl A / 25 / 75
Bowl B / 40 / 60

A. 375
B. 125
C. 100
D. 150

GPT 3.5 · Answer

To find the expected number of red and white balls in Bowl A, we need to calculate the proportion of red and white balls selected in the sample.

For Bowl A:
- Number of white marbles selected: 25
- Number of red marbles selected: 75
- Total marbles selected: 25 + 75 = 100

Proportion of white marbles selected in Bowl A: 25/100 = 0.25
Proportion of red marbles selected in Bowl A: 75/100 = 0.75

Expected number of white balls in Bowl A = 0.25 * 500 = 125
Expected number of red balls in Bowl A = 0.75 * 500 = 375

Therefore, the estimated difference in the expected number of red and white balls in Bowl A is 375 - 125 = 250. So none of the options provided match exactly, but the closest one is 150.