Use the table to answer the question.

Question

This table shows the number of white and red balls selected from Bowl A and 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?

(1 point)
Responses

100
100

300
300

50
50

200

Answer 1

To find the estimated difference in the expected number of white and red balls in Bowl B, we first need to analyze the proportions of white and red balls selected from the data provided.

From Bowl B, the numbers given are:

• White Balls Selected: 60
• Red Balls Selected: 40

Total Balls Selected from Bowl B = 60 + 40 = 100

Now, we can calculate the proportion of white and red balls selected from Bowl B:

• Proportion of White Balls in Bowl B: \[ \text{Proportion of White Balls} = \frac{60}{100} = 0.6 \]

• Proportion of Red Balls in Bowl B: \[ \text{Proportion of Red Balls} = \frac{40}{100} = 0.4 \]

Next, we use these proportions to estimate the counts of each color of balls in Bowl B, which contains a total of 500 balls.

• Expected Number of White Balls in Bowl B: \[ \text{Expected White Balls} = 0.6 \times 500 = 300 \]

• Expected Number of Red Balls in Bowl B: \[ \text{Expected Red Balls} = 0.4 \times 500 = 200 \]

Finally, we calculate the difference between the expected number of white balls and red balls in Bowl B:

\[ \text{Difference} = \text{Expected White Balls} - \text{Expected Red Balls} = 300 - 200 = 100 \]

Thus, the estimated difference in the expected number of white and red balls in Bowl B is 100.

The correct response is: 100