If a fowl is treated, probability of dying is 1/10 while if not treated the probability is 7/10 calculate the probability that, a fowl picked at random from the 36 fowl is
(i) Treated with the drug and will die
(ii) Not treated with the drug and will die
(iii) Not treated with the drug will not die
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
To calculate the probabilities, we can use the total probability rule. Let's break down the problem step by step:
Step 1: Calculate the probability of treating a fowl.
The probability of treating a fowl is not given in the question, so we need to calculate it. We know that the probability of dying if treated is 1/10, which implies the probability of surviving if treated is 1 - 1/10 = 9/10.
Therefore, the probability of treating a fowl is 9/10.
Step 2: Calculate the probability of not treating a fowl.
Since the probability of treating a fowl is 9/10, the probability of not treating a fowl is the complement: 1 - 9/10 = 1/10.
Therefore, the probability of not treating a fowl is 1/10.
Now, let's calculate the requested probabilities:
(i) Probability of a fowl being treated with the drug and dying:
The probability of a fowl being treated and dying is the product of the probabilities of being treated and dying. So, the probability is (9/10) * (1/10) = 9/100.
Therefore, the probability that a fowl picked at random from the 36 fowl is treated with the drug and will die is 9/100.
(ii) Probability of a fowl not being treated with the drug and dying:
The probability of a fowl not being treated and dying is the product of the probabilities of not being treated and dying. So, the probability is (1/10) * (7/10) = 7/100.
Therefore, the probability that a fowl picked at random from the 36 fowl is not treated with the drug and will die is 7/100.
(iii) Probability of a fowl not being treated with the drug and not dying:
The probability of a fowl not being treated and not dying is the product of the probabilities of not being treated and not dying. So, the probability is (1/10) * (3/10) = 3/100.
Therefore, the probability that a fowl picked at random from the 36 fowl is not treated with the drug and will not die is 3/100.