Answer to Question #218261 in Statistics and Probability for sly

Question

.A farmer produces seeds in packets for sale. The probability that a seed selected will grow is 0.8. If 5 of the seeds are grown, what is the probability that?:

i.less than two will grow? 

ii.less more than three will grow?

Answer 1

Binomial (5,0.8)

$P(x)=\binom{n}{x}P^x(1-P)^{n-x}, x=0,1,...,5.$

I $P(<2)$

$P(x<2)=P(x=0)+P(x=1)$

$=\binom{5}{0}(1-0.8)^{5}+\binom{5}{1}0.8(1-0.8)^{4}$

$=0.00032+0.0064$

$=0.672$

Ii. P(<3)

$P(x<3)=P(x=0)+P(x=1)+P(x=2)$

From part one, we already have $P(x=1)+P(x=0)=0.00672$

Thus,

$P(x<3)=0.00672+P(x=2)$

$=0.00672+\binom{5}{2}0.8^2(1-0.8)^{3}$

$=0.0672+0.0512$

$=0.05792$