To solve the problem of finding the probability that the sum of two randomly picked balls (marked 1-100) is even, follow these steps:

Key Observation:

The sum of two numbers is even if and only if both numbers are even OR both are odd.

Step 1: Count even and odd numbers

From 1 to 100:

• Even numbers: 50 (2,4,...,100)
• Odd numbers: 50 (1,3,...,99)

Step 2: Calculate favorable outcomes

Number of ways to pick 2 even balls: $\binom{50}{2} = \frac{50×49}{2} = 1225$
Number of ways to pick 2 odd balls: $\binom{50}{2} = 1225$
Total favorable outcomes: $1225 + 1225 = 2450$

Step 3: Total possible outcomes

Number of ways to pick 2 balls from 100: $\binom{100}{2} = \frac{100×99}{2} = 4950$

Step 4: Compute probability

Probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{2450}{4950} = \frac{49}{99}$

Answer: $\boxed{\dfrac{49}{99}}$

作者声明:本文包含人工智能生成内容。