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

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Answer 1 · 2017-03-28T12:43:31

$P (X = 10) = 0.7021 (4 d p)$ $P(X=10)=0.7021 (4dp)$

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

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