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Lets Make A Deal. Using Probability To Make Big Bucks Vinayak Ranade Massachusetts Institute of Technology. The Monty Hall Problem. The Right Choice. A. B. A B. Events And Conditional Probability. A. B. P(A | B) = P(A B). A B. P(B). Baye’s Rule. The Right Choice.
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Lets Make A Deal Using Probability To Make Big Bucks Vinayak Ranade Massachusetts Institute of Technology
A B A B Events And Conditional Probability
A B P(A | B) = P(A B) A B P(B) Baye’s Rule
The Right Choice A B The prize is behind door 1 and I reveal door 2 P(A B)=1/6 B I reveal door 2 P(B) = 1/2 A The prize is behind door 1 P(A) = 1/3 A | B = The prize is behind door 1 giventhat I reveal door 2
B I reveal door 2 P(B) = 1/2 A B The prize is behind door 1 and I reveal door 2 P(A B)=1/6 A The prize is behind door 1 P(A) = 1/3 P(A | B) = P(A B) = 1/3 P(B) The Right Choice
Probability Mass Functions And Expectation Event A Result 1 : Probability 1 (p1) Result 2 : Probability 2 (p2) … Result N : Probability N (pN) Expectation(A) = r1 * p1 + r2 * p2 + … + rN * pN