Maximum Probability of a Pair of Same Color

In order to find the maximum probability of a pair of the same color among Mr. Bean's magical balls, we need to consider the different color combinations after some of the balls have turned white due to rain.

Given Information:
- 25 pink balls
- 10 green balls
- 31 red balls
- 31 yellow balls
- 30 purple balls
- Red, green, and yellow balls turn into white when drenched in rain

Color Combinations:
1. Before raining:
- Pink: 25
- Green: 10
- Red: 31
- Yellow: 31
- Purple: 30

2. After raining:
- Pink: 25
- Green: 0 (turned white)
- Red: 0 (turned white)
- Yellow: 0 (turned white)
- Purple: 30

Calculating the Maximum Probability:
To find the maximum probability of a pair of the same color, we need to consider the worst-case scenario, where the number of balls of the same color is minimized.

Let's consider the worst-case scenario for each color:

1. Pink:
- Since there are 25 pink balls, the worst-case scenario is that each pink ball pairs with a different color ball, except for one.
- Therefore, there will be 24 pink balls without a pair.

2. Green, Red, and Yellow:
- Since all the green, red, and yellow balls turn into white when drenched in rain, they won't contribute to the maximum probability of a pair of the same color.
- Therefore, the worst-case scenario is that all green, red, and yellow balls are removed, resulting in 0 balls of each color.

3. Purple:
- Since there are 30 purple balls, the worst-case scenario is that each purple ball pairs with a different color ball, except for one.
- Therefore, there will be 29 purple balls without a pair.

Calculating the Maximum Probability using Worst-Case Scenario:
To calculate the maximum probability of a pair of the same color, we need to consider the number of balls remaining after the worst-case scenario for each color:

- Pink: 25 - 24 (worst-case scenario) = 1 ball
- Green: 0 (worst-case scenario)
- Red: 0 (worst-case scenario)
- Yellow: 0 (worst-case scenario)
- Purple: 30 - 29 (worst-case scenario) = 1 ball

Calculating the Probability:
The maximum probability of a pair of the same color can be calculated using the formula:
Probability = (Number of balls with a pair) / (Total number of balls)

In this case, the number of balls with a pair is 2 (1 pink ball and 1 purple ball), and the total number of balls is 2.

Probability = 2 / 2 = 1

However, the answer given is '64'. Based on the information provided, it is not possible to determine how '64' is obtained as the maximum probability. Therefore, the given answer may be incorrect or there might be some missing information.