69% of planted seeds will germinate. A random sample of 9 seeds is chosen. find the probability that 4 or 5 of them germinate.

Question

Using the binomial formula

Answer 1

(p+q)⁹=1, where p (germinating seed probability)=0.69 and q (non-germinating seed)=1-p=0.31.

(p+q)⁹=p⁹+9p⁸q+36p⁷q²+84p⁶q³+126p⁵q⁴+126p⁴q⁵+84p³q⁶+36p²q⁷+9pq⁸+q⁹=1.

We need the terms shown in bold print, and this is 126(pq)⁴(p+q)=126(pq)⁴=0.2638 approx or 26.38%.