Calculation process: the survival probability of 18 tree is equal to 18 tree among 20 trees, and the survival probability of each tree is 90%=0.9, so the death probability of each small tree is 0. 1= 10%, so 18 tree can survive.
c(20, 18)*90%^ 18* 10%^2=c(20, 18)*0.9^ 18*0. 1^2=(20* 19/2)*(0.9)^ 18*(0. 1)^2
= 190*(0.9)^ 18*(0.0 1)
=0.285, then the probability that these small trees can survive 18 is 29%.
Extended data:
Hypergeometric distribution Note:
The model of 1 and hypergeometric distribution is irreplaceable sampling.
2. The parameters in the hypergeometric distribution are m, n, n, and the hypergeometric distribution is denoted as X~H(n, m, n).
Hypergeometric distribution theorem;
1, for hypergeometric distribution X~H(N, m, n), the mathematical expectation of random variable x ex = n * m/n.
2. The variance of hypergeometric distribution, for X~H(N, m, n), dx = n * m/n * (1-m/n) * [(n-n)/(n-1)].
The relationship between hypergeometric distribution and binomial distribution;
1. In hypergeometric distribution, when n approaches infinity, M/N tends to p (p in binomial distribution).
2. When n approaches infinity, the hypergeometric distribution is approximately binomial.
Baidu Encyclopedia-Hypergeometric Distribution