Answer to Question #344907 in Statistics and Probability for kay

Question

A tree if less than three feet high and when transplanted has a 40% chance of survival. If six such trees are transplanted, what is the probability that at most four five will not survive?

Answer 1

Let $X=$ the number of trees which will not survive: $X\sim Bin (n, p).$

Given $n=6, p=1-0.4=0.6, q=0.4.$

a.

$$P(X\le4)=1-P(X=5)-P(X=6)$$

$$=1-\dbinom{6}{5}(0.6)^{5}(0.4)^{6-5}-\dbinom{6}{6}(0.6)^{6}(0.4)^{6-6}$$

$$=0.54432$$

b.

$$P(X\le5)=1-P(X=6)$$

$$=1-\dbinom{6}{6}(0.6)^{6}(0.4)^{6-6}=0.953344$$