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

1 Answer
Mar 28, 2017

P(X=10)=0.7021 (4dp)P(X=10)=0.7021(4dp)

Explanation:

assuming the germination of each seed is an independent event, we have a Binomial distribution

X~B(n,p)X~B(n,p)

"where "n=" number of seeds planted"where n= number of seeds planted

" and "p="probability of germination" and p=probability of germination

:.X~B(12,0.96)

P(X=k)=((12),(k))0.96^k0.04^(12-k)

in this case we have

P(X=10)=((12),(10))0.96^10 0.04^2

using a calculator we we have

P(X=10)=66xx0.664832636xx0.0016

#P(X=10)=0.7020632636

P(X=10)=0.7021 (4dp)