Gregor Mendel conducted his famous hydridization experiments and used peas with

Question

Gregor Mendel conducted his famous hydridization experiments and used peas with green pods and peas with yellow pods. Because green is dominant and yellow is recessive, when crossing two parents with the green/yellow pair of genes, we expect that ¾ of the offspring peas should have green pods. That is, P(green pod)=3/4. Assume that all parents have the green/yellow combination of genes

1) find the probability that exactly three of five offspring peas have green pods.

2) find the probability that at least one of five offspring peas have green pods.

3) find the mean and standard deviation for the numbers of peas with green pods when groups of 5 offspring peas are generated.

Explanation / Answer

let X=numbers of peas with green pods

here we use binomial distribution with parameter n and p and for

Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

(1) here p=P(green pod)=3/4 and n=5

P(X=3)=5C3(0.75)3(1-0.75)5-3   =0.2637 ( using ms-excel commmand=BINOMDIST(3,5,0.75,0))

(2) here n=5, p=0.75

P(X=at least 1)=P(X>1)=1-P(X<=1)=1-0.0156=0.9844

P(X<=1)=0.0156 (  using ms-excel commmand=BINOMDIST(1,5,0.75,1))

(3) for binomial distribution E(X)=mean=np and Variance(X)=np(1-p)

mean=np=5*0.75=3.75

standard deviation=sqrt(np(1-p))=sqrt(5*0.75*(1-0.75))=0.9682

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