Karina and Selena are suspected for a certain crime and was imprisoned separately such that any kind of communication between them is prohibited. But the police doesn’t have enough evidence to convict them with a principal charge so the police thought of an idea and offer each suspects a bargain: (i) If Karina and Selena both betray each other, each of them serves 3 years in prison. (ii) If Karina betrays Selena but Selena remains silent, Karina will be set free and Selena will serve 5 years in prison. (iii) If Selena betrays Karina but Karina remains silent, Selena will be set free and Karina will serve 5 years in prison. (iv) If Karina and Selena both remain silent, both of them will only serve 1.5 years in prison. It is observed that the probability of Karina betraying Selena and Selena remaining silent is equal to the probability of Selena betraying Karina and Karina remaining silent. The probability of them both betraying each other is twice as much as the probability of Karina betraying Selena and Selena remaining silent. The probability of them both remaining silent is half as much as the probability of Karina betraying Selena and Selena remaining silent. (a) Construct the probability distribution of the random variable X, where X is the number of years Selena will serve in prison. (b) Find the expected number of years Selena will serve in prison.
Karina and Selena are suspected for a certain crime and was imprisoned separately such that any kind of
communication between them is prohibited. But the police doesn’t have enough evidence to convict them with a principal charge so the police thought of an idea and offer each suspects a bargain:
(i) If Karina and Selena both betray each other, each of them serves 3 years in prison.
(ii) If Karina betrays Selena but Selena remains silent, Karina will be set free and Selena will serve 5 years in prison.
(iii) If Selena betrays Karina but Karina remains silent, Selena will be set free and Karina will serve 5 years in prison.
(iv) If Karina and Selena both remain silent, both of them will only serve 1.5 years in prison.
It is observed that the probability of Karina betraying Selena and Selena remaining silent is equal to the probability of Selena betraying Karina and Karina remaining silent. The probability of them both betraying each other is twice as much as the probability of Karina betraying Selena and Selena remaining silent. The probability of them both remaining silent is half as much as the probability of Karina betraying Selena and Selena remaining silent.
(a) Construct the probability distribution of the random variable X, where X is the number of years Selena will serve in prison.
(b) Find the expected number of years Selena will serve in prison.
Step by step
Solved in 3 steps with 4 images
