Conditional Probability & Conditional Expectations Compute - PowerPoint PPT Presentation

Conditional Probability & Conditional Expectations Compute Probabilities by Conditioning IE 502: Probabilistic Models Jayendran Venkateswaran IE & OR

Gambler’s Chances • A gambler has Rs.300 in his pocket when he walks into a casino. He plays a game in which the probability he gains Rs.100 is 1/3, the probability that he gains Rs.200 is 1/6, and the probability that he loses Rs.100 is 1/2. He decides ahead of time that he will stop playing as soon as he has enough money to buy a Rs.500 toy for his daughter. Of course, he also must stop playing if he goes broke! – What is the probability that he goes broke? …buys toy? – What is the expected number of games he plays before he leaves the casino? IE502: Probabilistic Models IEOR @ IITBombay

Welcome to the game show! a.k.a Monty Hall • We have two goats and a car. • They are placed randomly behind closed doors. • You, the contestant, need to pick a door, & win what’s inside! • But with a twist.. IE502: Probabilistic Models IEOR @ IITBombay

Game show a.k.a Monty Hall • You are given a choice of 3 doors. Behind one door is a car & behind the other two, goats • What’s the probability of winning a car? IE502: Probabilistic Models IEOR @ IITBombay

Game show a.k.a Monty Hall • You are given a choice of 3 doors. Behind one door is a car & behind the other two, goats P{Car} = 1/3 P{Car} = 1/3 P{Car} = 1/3 • What’s the probability of winning a car? IE502: Probabilistic Models IEOR @ IITBombay

Game show a.k.a Monty Hall • You choose a door Say, door 3 [door 3 remains closed] • The twist … IE502: Probabilistic Models IEOR @ IITBombay

Game show a.k.a Monty Hall • You choose a door say, door 3 [door 3 remains closed] • The twist … • I open one of the remaining doors [either 1 or 2] to reveal a goat IE502: Probabilistic Models IEOR @ IITBombay

Game show a.k.a Monty Hall • You choose a door say, door 3 [door 3 remains closed] • The twist … • I open one of the remaining doors [either 1 or 2] to Now, “ Do you wish to stay reveal a goat with your original choice (door3) or switch (to door1)?” IE502: Probabilistic Models IEOR @ IITBombay

Game show a.k.a Monty Hall • You choose a door say, door 3 [door 3 remains closed] • The twist … • I open one of the P{Car} = ? P{Car} = 0 P{Car} = ? remaining doors [either 1 or 2] to Now, “ Do you wish to stay reveal a goat with your original choice (door3) or switch (to door1)?” IE502: Probabilistic Models IEOR @ IITBombay