A poultry farmer vaccinated 540 of his 720 chickens against a disease. Two months later, 5% of the vaccinated and 80% of the unvaccinated chicken, contracted the disease.
Calculate the probability that a chicken chosen random contracted the disease.
(.05*540 + .80*(720-540))/720 = 23.75%
To calculate the probability that a randomly chosen chicken contracted the disease, we'll need to consider two scenarios: chickens that were vaccinated and chickens that were not vaccinated.
First, let's calculate the number of chickens that were vaccinated but still contracted the disease. We know that 5% of the vaccinated chickens contracted the disease, so we can calculate the number of vaccinated chickens that contracted the disease as follows:
Number of vaccinated chickens that contracted the disease = (5% of vaccinated chickens) = (5/100) * 540
Next, let's calculate the number of chickens that were not vaccinated and contracted the disease. We know that 80% of the unvaccinated chickens contracted the disease, so we can calculate the number of unvaccinated chickens that contracted the disease as follows:
Number of unvaccinated chickens that contracted the disease = (80% of unvaccinated chickens) = (80/100) * (720 - 540)
Now, we can calculate the total number of chickens that contracted the disease by adding the number of vaccinated chickens and the number of unvaccinated chickens that contracted the disease:
Total number of chickens that contracted the disease = (Number of vaccinated chickens that contracted the disease) + (Number of unvaccinated chickens that contracted the disease)
Finally, we can calculate the probability of selecting a chicken at random that contracted the disease by dividing the total number of chickens that contracted the disease by the total number of chickens:
Probability = (Total number of chickens that contracted the disease) / (Total number of chickens)
Now let's substitute the values and calculate:
Number of vaccinated chickens that contracted the disease = (5/100) * 540 = 27
Number of unvaccinated chickens that contracted the disease = (80/100) * (720 - 540) = 57.6
Total number of chickens that contracted the disease = 27 + 57.6 = 84.6
Total number of chickens = 720 (since this is the total number of chickens on the farm)
Probability = 84.6 / 720 ≈ 0.1175
Therefore, the probability that a randomly chosen chicken contracted the disease is approximately 0.1175 or 11.75%.