First, we need to find the total number of balls in Bowl A. Since Bowl A contains 45 white balls and 55 red balls, the total number of balls in Bowl A is 45 + 55 = 100.
Next, we can find the ratio of white balls to total balls in Bowl A by dividing the number of white balls by the total number of balls: 45 / 100 = 0.45.
We can then use this ratio to estimate the number of white balls in Bowl B. Since Bowl B contains 500 balls, we estimate that Bowl B contains 0.45 * 500 = 225 white balls.
Similarly, we can estimate the number of red balls in Bowl B by subtracting the estimated number of white balls from the total number of balls in Bowl B: 500 - 225 = 275 red balls in Bowl B.
Finally, we can 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: 225 - 275 = -50.
Therefore, the estimated difference in the expected number of white and red balls in Bowl B is -50.