Statistics I20805 marksNumerical: Conditional probabilityBayes theorem
What is conditional probability? Three roads A, B and C lead away from a jail. A prisoner escaping from the jail selects a road at random. If road A is selected, the probability of escaping is 1/10. Similarly for road B it is 1/8 and for road C it is 1/5. i. What is the probability that the prisoner
What is conditional probability? Three roads A, B and C lead away from a jail. A prisoner escaping from the jail selects a road at random. If road A is selected, the probability of escaping is 1/10. Similarly for road B it is 1/8 and for road C it is 1/5. i. What is the probability that the prisoner will succeed in escaping? ii. If the prisoner has succeeded in escaping, what is the probability that he had chosen the road A? [5]
- Roads: A, B, C selected at random, so $P(A) = P(B) = P(C) = \dfrac{1}{3}$ - $P(E \mid A) = \dfrac{1}{10}$ - $P(E \mid B) = \dfrac{1}{8}$ - $P(E \mid C) = \dfrac{1}{5}$ where $E$ = event of escaping. Conditional probability is the probability of an event occurring given that another event has al...