Seeds are often treated with a fungicide for protection in poor-draining, wet en
ID: 3334264 • Letter: S
Question
Seeds are often treated with a fungicide for protection in poor-draining, wet environments. In a small-scale trial prior to a large-scale experiment to determine what dilution of the fungicide to apply, four treated seeds and six untreated seeds were planted in clay soil and the number of plants emerging from the treated and untreated seeds were recorded. Suppose the dilution was not effective and only four plants emerged. Let x represent the number of plants that emerged from treated seeds. (Round your answers to three decimal places.) (a) Find the probability that x = 4. (b) Find P(x 3). (c) Find P(2 x 3).
Explanation / Answer
Solution:
Given x represent the number of plants that emerged from treated seeds.
here N = Total number of seeds = 10
M = Number of treated seeds = 4
N = Number of untreaded seeds = 6
(a) P(x = 4) = 4C4 * 6C0/ 10C4 = 1 * 1/210 = 0.0047
(b) P(x 3) = 1 - P(x >3) = 1 - 0.0.0047 = 0.9952
(c) P(2 x 3) = p(x = 2) + p(x = 3)
= 4C2 * 6C2/10C4 + 4C3 * 6C1/ 10C4
= 6*15/210 + 4*6/210 = 0.4285 + 0.1142 = 0.543