Question

A packet of vegetables seeds has a germination rate of 96%. What is the probability that exactly 10 of 12 seeds planted will sprout?

Answer 1

Given :

Probability of success = p = 0.96

Number of sample = n = 12

Let X be the number of seeds planted will sprout.

X ~ Binomial (n=12, p=0.96)

The probability density function of Binomial distribution is given by

P(X=x) = (nCx) * p^x * (1-p)^n-x

Ghe probability that exactly 10 of 12 seeds planted will sprout :

P(X=10) = (12C10) * (0.96)^10 * (1-0.96)^12-10

= (12C10) * (0.96)^10 * 0.04^2

= 0.0702

P(X=10) = 0.0702

Therefore the probability that exactly 10 of 12 seeds planted will sprout is 0.0702