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 (4dp)#

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

#X~B(n,p)#

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

#" 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)#