Question

315 ducks in a wetland are tested for a disease. 14 of them test positive for the disease. the empirical probability that a randomly chosen ducks will test positive is the empirical probability that a randomly chosen ducks will test negative is (note: enter each answer as a fraction or as a decimal rounded to the nearest thousandth.)

Explanation:

Step1: Recall probability formula

The formula for empirical probability is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Calculate positive - test probability

The total number of ducks is $n = 315$, and the number of ducks that test positive is $m_1=14$. So the empirical probability of a duck testing positive, $P(\text{positive})=\frac{14}{315}=\frac{2}{45}\approx0.044$.

Step3: Calculate negative - test probability

The number of ducks that test negative is $m_2=315 - 14=301$. So the empirical probability of a duck testing negative, $P(\text{negative})=\frac{301}{315}=\frac{43}{45}\approx0.956$.

Answer:

The empirical probability that a randomly - chosen duck will test positive is $\frac{2}{45}\approx0.044$.
The empirical probability that a randomly - chosen duck will test negative is $\frac{43}{45}\approx0.956$.