Answer to Question #335011 in Statistics and Probability for Tona

Question

A producer of new corn seed guarantees that 85% of the seeds will germinate. A gardener plants 10 of the seeds. What is the probability that;

a) None will grow

b) Six will grow

c) At least nine will grow

Answer 1

Let $X=$ the number of corn seed which growed: $X\sim Bin (n, p).$

Given $p=0.85, q=1-p=0.15, n=10.$

a)

$$P(X=0)=\dbinom{10}{0}(0.85)^0(0.15)^{10-0}$$

$$\approx5.7665\times10^{-9}$$

b)

$$P(X=6)=\dbinom{10}{6}(0.85)^6(0.15)^{10-6}$$

$$\approx0.0401$$

c)

$$P(X\ge9)=P(X=9)+P(X=10)$$

$$=\dbinom{10}{9}(0.85)^9(0.15)^{10-9}+\dbinom{10}{10}(0.85)^{10}(0.15)^{10-10}$$

$$\approx0.5443$$