A researcher chooses three leaves from a target environment and classifies each sample as fungus-free or contaminated. Suppose that a leaf has a probability of 0.4 of being infected. Find the probability, that two leaves infected.
A) 0.490
B) 0.181
C) 0.314
D) 0.144
E) 0.288

Question

A researcher chooses three leaves from a target environment and classifies each sample as fungus-free or contaminated. Suppose that a leaf has a probability of 0.4 of being infected. Find the probability, that two leaves infected. ​
A) 0.490
B) 0.181
C) 0.314
D) 0.144
E) 0.288

Quizplus · Accepted Answer

The probability of exactly two leaves being infected can be calculated using the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n=3, k=2, and p=0.4. This gives P(2 infected) = C(3, 2) * (0.4)^2 * (0.6)^1 = 3 * 0.16 * 0.6 = 0.288.

A Researcher Chooses Three Leaves from a Target Environment and Classifies