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 consider the total number of outcomes for each situation.
There are 36 fowls in total, and we are given the probabilities of dying if treated and not treated. Let's calculate the probabilities for each situation:
(i) Treated with the drug and will die:
The probability of dying if treated is 1/10. Therefore, the probability of a fowl being treated and dying is (1/10) * 36. Simplifying this expression, we get 3.6 or 18/5.
(ii) Not treated with the drug and will die:
The probability of dying if not treated is 7/10. Therefore, the probability of a fowl not being treated and dying is (7/10) * 36. Simplifying this expression, we get 25.2 or 252/10.
(iii) Not treated with the drug and will not die:
The probability of not dying if not treated is 1 - 7/10, which is 3/10. Therefore, the probability of a fowl not being treated and not dying is (3/10) * 36. Simplifying this expression, we get 10.8 or 54/5.
To summarize:
(i) The probability of a fowl being treated with the drug and dying is 18/5.
(ii) The probability of a fowl not being treated with the drug and dying is 252/10.
(iii) The probability of a fowl not being treated with the drug and not dying is 54/5.