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Variable Change - Big words for conditional Probability Calc

problem is explained in http://www.youtube.com/watch?v=6Rl_p3JlSd0

When you pick 1 door, the Probabilities are :

P(car)=1/3

P(Goat 1)=1/3

P(Goat 2)=1/3

Now, Monty opens a door with a goat,

Switching your choice means "What is the probability that the other door is the car ?"

OR : you originally took the car AND switch

P(successful switch under this knowledge)=0,

P(successful switch/you took the car) = 1/3 x 0

OR : you originally took Goat 1 AND switch

P(successful switch under this knowledge)=1

P(successful switch/you took Goat 1)=1/3x1

OR : you originally took Goat 2 and switch

P(successful switch under this knowledge)=1

P(succcessful switch/you took Goat 1)=1

OR = +

so P(successful switch/you took random door) = 1/3x0 + 1/3x1 + 1/3x1

= 2/3

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