Question #335011

A producer of new corn seed guarantees that 85% of the seeds will germinate. A gardener plants 10 of the seeds. What is the probability that;

a) None will grow

b) Six will grow

c) At least nine will grow


1
Expert's answer
2022-04-29T14:40:05-0400

Let X=X= the number of corn seed which growed: XBin(n,p).X\sim Bin (n, p).

Given p=0.85,q=1p=0.15,n=10.p=0.85, q=1-p=0.15, n=10.

a)


P(X=0)=(100)(0.85)0(0.15)100P(X=0)=\dbinom{10}{0}(0.85)^0(0.15)^{10-0}

5.7665×109\approx5.7665\times10^{-9}

b)


P(X=6)=(106)(0.85)6(0.15)106P(X=6)=\dbinom{10}{6}(0.85)^6(0.15)^{10-6}

0.0401\approx0.0401

c)


P(X9)=P(X=9)+P(X=10)P(X\ge9)=P(X=9)+P(X=10)

=(109)(0.85)9(0.15)109+(1010)(0.85)10(0.15)1010=\dbinom{10}{9}(0.85)^9(0.15)^{10-9}+\dbinom{10}{10}(0.85)^{10}(0.15)^{10-10}

0.5443\approx0.5443

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