Question

A seedling supplier sells equal proportions of pine and fir seedlings (50% each). Based on historical evidence, the following probabilities pertaining to the mortality rates of seedlings are also known:
P (seedling will not survive) = 0.05, P (seedling is a pine AND it will not survive) = 0.03
a) If a dead seedling has been found, what is the probability that it was a fir?

b) All of the pine seedlings that survive are immediately planted. However, in a typical pine plantation, only 10% of the planted seedlings survive past the age of one year. If 400 pine seedlings are randomly selected from the plantation at the end of year I, what is the probability that less than 30 will not survive?

Answer 1

a)P( seedling is a fir AND it will not survive) = P (seedling will not survive) - P (seedling is a pine AND it will not survive) =0.05-0.03 =0.02

hence probability that it was a fir given dead seedling

=P( seedling is a fir AND it will not survive) / P (seedling will not survive) =0.02/0.05=0.40

b)

n=	400	p=	0.1000
here mean of distribution=μ=np=		40
and standard deviation σ=sqrt(np(1-p))=		6.0000

for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:: P(X<30)=P(Z<(30-40)/6)=P(Z<-1.67)=0.0475