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, we need to use the concept of conditional probability.
Let's break down the information given:
- Probability of dying if treated: 1/10
- Probability of dying if not treated: 7/10
We are given that there are 36 fowl in total. Let's calculate the probabilities using the given information:
(i) Probability that a fowl picked at random is treated with the drug and will die:
This can be calculated as the product of the probability of being treated (1/36) and the probability of dying if treated (1/10).
Probability = (1/36) * (1/10) = 1/360
(ii) Probability that a fowl picked at random is not treated with the drug and will die:
This can be calculated as the product of the probability of not being treated (35/36) and the probability of dying if not treated (7/10).
Probability = (35/36) * (7/10) = 245/360
(iii) Probability that a fowl picked at random is not treated with the drug and will not die:
This can be calculated as the product of the probability of not being treated (35/36) and the probability of not dying if not treated (3/10).
Probability = (35/36) * (3/10) = 105/360
Therefore, the probabilities are:
(i) Treated with the drug and will die: 1/360
(ii) Not treated with the drug and will die: 245/360
(iii) Not treated with the drug and will not die: 105/360