To calculate the probabilities, let's represent the events as follows:
T = Treated with the drug
NT = Not treated with the drug
D = Fowl will die
Given:
Probability of dying if treated (P(D|T)) = 1/10
Probability of dying if not treated (P(D|NT)) = 7/10
We need to calculate the following probabilities:
(i) Probability of picking a fowl that is treated with the drug and will die (P(T and D)):
P(T and D) = P(D|T) * P(T)
Since the fowl is picked at random, the probability of picking a fowl that is treated (P(T)) is 1/36 (since there are 36 fowls in total).
P(T and D) = (1/10) * (1/36) = 1/360
(ii) Probability of picking a fowl that is not treated with the drug and will die (P(NT and D)):
P(NT and D) = P(D|NT) * P(NT)
P(NT and D) = (7/10) * (35/36) = 245/360
(iii) Probability of picking a fowl that is not treated with the drug and will not die (P(NT and ~D)):
P(NT and ~D) = P(~D|NT) * P(NT)
Since the fowl will either die or not die, we can use the complement rule to calculate P(NT and ~D):
P(NT and ~D) = 1 - P(NT and D)
P(NT and ~D) = 1 - (245/360) = 115/360
Therefore, the probabilities are:
(i) P(T and D) = 1/360
(ii) P(NT and D) = 245/360
(iii) P(NT and ~D) = 115/360