suppose James and Joy is the prisoner to be freed and any of the five prisoners can come for the trail. what is the probability that in the two prisoners will be executed in sequentially

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4. Five prisoners, Jack, Jill, John, Joy and James, are held in separate cells. Police knows specifically that out of the five, three prisoners are to be executed and two will be freed but prisoners have no idea about who will be executed and who will be free. Each prisoner is brought to trail at a gap of one hour in a random manner. What is the probability that:

(a) [1 Marks] Suppose James and Joy is the prisoner to be freed and any of the five prisoners can come for the trail. What is the probability that in the two prisoners will be executed in sequentially.

(b) [2 Marks] Suppose James and Jill are already given their verdict. Now, Joy is given the information that: The probability for him to be free is 1/3. And at least one of John and Jill will be executed. If he gets the information about one of the prisoner who will be executed from the police, the probability of his execution will be half. Thus, his chance of being free will be high. Investigate Joy’s thinking. 2

(c) [2 Marks] Suppose James and Jill are given their verdict. Now, the policeman forgets that the name of the person to be executed and freed. In trials, prisoners are assigned random verdict. Find the probability that each person receives correct verdict.

(d) [2 Marks] Suppose we now consider 50 prisoners and every prisoner knows the verdict of prisoner presented in the trail before him (For e.g., Fifth prisoner knows the verdict for all the 4 prisoners before him). In each case, if the prisoner will be able to guess correctly about his trial, he will be freed else will be executed. Formulate a strategy for the prisoners such that no prisoner is executed.

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