Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

ILIA wrote:

Let's say I originally picked door 1 then door 2 was opened showing the goat so we want to calculate probability of car behind door 1 given that door 2 has a goat and probability of car behind door 3 given that door 2 has a goat.

The flaw in your problem definition is the condition *"given that door 2 has a goat"*, it should be *"given Monty opens Door 2"*

.

If we call the 'probability that Monty opens Door 2', p(g2), then:

p(g2) = (1/3*1) + (1/3 * 1/2) + (1/3 * 0) = 1/2 and

p(g2)|(c1) = 1/2 and p(g2)|(c3) = 1

Plug those values into Bayes and you get 1/3 and 2/3

Pages: **1**