Answer to Question #293818 in Statistics and Probability for Jojo

Question

A certain type of ochro seed germinates 75% of the time. A backyard farmer planted 6 seeds. What is the probability that more than 4 seeds germinate?

Answer 1

Let $X=$ the number of seeds which germinate: $X\sim Bin (n, p).$

Given $n=6, p=0.75, q=1-p=1-0.75=0.25$

$$P(X>4)=P(X=5)+P(X=6)$$

$$=\dbinom{6}{5}(0.75)^5(0.25)^{6-5}+\dbinom{6}{6}(0.75)^6(0.25)^{6-6}$$

$$=0.35595703125+0.177978515625$$

$$\approx 0.5339$$