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) all four plants emerged from treated seeds? b) three or fewer emerged from treated seeds? c) at least one emerged from untreated seeds?

Answer 1

The probability that all four plants emerged from treated seeds is 1/625. The probability that three or fewer plants emerged from treated seeds is 340/625. The probability that at least one plant emerged from untreated seeds is 278/625.

Step-by-step explanation:

To calculate probabilities in this scenario, we need to understand that there were five treated and five untreated seeds, and only four plants actually sprouted. Let's answer each part of the question:

a) To find the probability that all four plants emerged from treated seeds, we need to calculate the probability of one plant emerging from a treated seed and multiply it by itself four times. Since there were five treated seeds, the probability of one plant emerging from a treated seed is 1/5. Therefore, the probability that all four plants emerged from treated seeds is (1/5) * (1/5) * (1/5) * (1/5) = 1/625.

b) To find the probability that three or fewer plants emerged from treated seeds, we need to calculate the probability that zero, one, two, or three plants emerged from treated seeds. The probability of zero plants emerging from treated seeds is (4/5) * (4/5) * (4/5) * (4/5) = 256/625. The probability of one plant emerging from treated seeds is (1/5) * (4/5) * (4/5) * (4/5) = 64/625. The probability of two plants emerging from treated seeds is (1/5) * (1/5) * (4/5) * (4/5) = 16/625. The probability of three plants emerging from treated seeds is (1/5) * (1/5) * (1/5) * (4/5) = 4/625. Adding these probabilities together, we get (256/625) + (64/625) + (16/625) + (4/625) = 340/625.

c) To find the probability that at least one plant emerged from untreated seeds, we need to calculate the probability that either one, two, three, four, or five plants emerged from untreated seeds.

The probability of one plant emerging from untreated seeds is (1/5) * (4/5) * (4/5) * (4/5) = 256/625 (as calculated in part b).

The probability of two plants emerging from untreated seeds is (1/5) * (1/5) * (4/5) * (4/5) = 16/625 (as calculated in part b).

The probability of three plants emerging from untreated seeds is (1/5) * (1/5) * (1/5) * (4/5) = 4/625 (as calculated in part b).

The probability of four plants emerging from untreated seeds is (1/5) * (1/5) * (1/5) * (1/5) = 1/625. The probability of five plants emerging from untreated seeds is (1/5) * (1/5) * (1/5) * (1/5) = 1/625.

Adding these probabilities together, we get (256/625) + (16/625) + (4/625) + (1/625) + (1/625) = 278/625.

Answer 2

c

Step-by-step explanation: