Question

In a field 20 percent of plants atlre infected.A random sample of 4 plants is selected.What is the probability that at most 3 are infected

Answer 1

Given : in a  field 20 percent of plants infected .  random sample of 4 plants is selected

To find : probability that at most 3 are infected

Solution:

field 20 percent of plants infected

Probability of infected p = (20/100) = 0.2

probability not infected q = 1 -  p = 1  -0.2 = 0.8

Sample of 4 plants => n = 4

P(x) = ⁿCₓpˣqⁿ⁻ˣ

probability that at most 3 are infected

= P(0) + P(1) + P(2) + P(3)

= 1  -  P(4)

=  1  - ⁴C₄(0.2)⁴(0.8)⁴⁻⁴

= 1  -  1 * 0.0016 * 1

= 0.9984‬

probability that at most 3 are infected =  0.9984‬

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