When planting trees, 20% of the seedlings do not survive. We need to find the most probable number of surviving seedlings out of 1000 planted seedlings.

1. Problem Description

When planting trees, 20% of the seedlings do not survive. We need to find the most probable number of surviving seedlings out of 1000 planted seedlings.

2. Solution Steps

Let $n$ be the number of planted seedlings, so $n = 1000$.

Let $p$ be the probability of a seedling surviving. Since 20% of the seedlings do not survive, 80% do survive. Thus, $p = 1 - 0.20 = 0.80$.

Let $q$ be the probability of a seedling not surviving, so $q = 0.20$.

We are looking for the most probable number of surviving seedlings, which we denote by $m_0$. The most probable number $m_0$ satisfies the following condition:

$np - q \le m_0 \le np + p$

Plugging in the values:

$1000 \times 0.8 - 0.2 \le m_0 \le 1000 \times 0.8 + 0.8$

$800 - 0.2 \le m_0 \le 800 + 0.8$

$799.8 \le m_0 \le 800.8$

Since $m_0$ must be an integer, the most probable number of surviving seedlings is $m_0 = 800$.

3. Final Answer

The most probable number of surviving seedlings is 800.