Question

Seed are often treated with fungicides to protect them in poor draining, wet environments. A small-scale trial, involving five treated and five untreated seeds, was conducted prior to a large-scale experiment to explore how much fungicide to apply. The seeds were planted in wet soil, and the number of emerging plants were counted. If the solution was not effective and four plants actually sprouted, what is the probability that a b c all four plants emerged from treated seeds

Answer 1

Answer:

2.38%

Step-by-step explanation:

Given that:

The population size involving numbers of treated and untreated seeds N  = 10

the number of seeds that are treated which are observed = 5

the number of seeds that sprouted 'n' = 4

Now, use the method of hypergeometric probability, we have the formula:

$p(y) = \dfrac{(^r_y)(^{N-r}_{n-y})}{(^N_n)}$

∴

$p(4) = \dfrac{(^5_4)(^{5}_{0})}{(^{10}_4)}$

$p(4) = \dfrac{\dfrac{5!}{4!(5-4)!}* \dfrac{5!}{0!(5-0)!} }{\dfrac{10!}{4!(10-4)!} }$

$p(4) = \dfrac{\dfrac{5!}{4!}* \dfrac{5!}{(5)!} }{\dfrac{10!}{4!(6)!} }$

$p(4) = \dfrac{5*1 }{210}$

p(4) = 0.0238

p(4) = 2.38%