If these seeds are planted according to the instructions, find the probability that more than 7 of them germinate.

Question

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 69% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that more than 7 of them germinate.

Answer 1

p=0.69, probability of success; 1-p=0.31, probability of failure.

(p+(1-p))⁹=1=p⁹+9p⁸(1-p)+36p⁷(1-p)²+84p⁶(1-p)³+126p⁵(1-p)⁴+126p⁴(1-p)⁵+84p³(1-p)⁶+36p²(1-p)⁷+9p(1-p)⁸+(1-p)⁹.

Each term gives the probability of each outcome: exponent of p is the number of successes.

The sum of the probabilities of the first two terms is the probability of more than 7 successes.

So p⁹+9p⁸(1-p) = p⁸(p+9-9p)= p⁸(9-8p) = 0.0514(9-5.52) = 0.0514×3.48 = 0.1788 = 17.88% approx.