# mt2solns - York University MATH 2030 3.0AF (Elementary...

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York University MATH 2030 3.0AF (Elementary Probability) Midterm 2 October 30, 2006 – Salisbury NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are four questions, on three pages. No other books or notes may be used. You may use a calculator. Show all your work, and explain or justify your answers. You may leave numerical answers unsimpliﬁed. 1. [20] A bag contains 5 dice. Four of them are standard fair dice. But the ﬁfth has the numbers 2–3–3–4–5–6 marked on its sides (ie there is no side showing a 1, but there are two sides showing 3’s). I pick a die at random from the bag, and roll it twice. Given that I get two 3’s, what is the conditional probability the die is fair? Solution: Let B be the event that the die is fair, and let A be the event that we roll two 3’s. Then we know that P ( B ) = 4 5 P ( B c ) = 1 5 P ( A | B ) = 1 6 × 1 6 = 1 36 P ( A | B c ) = 2 6 × 2 6 = 4 36 So by Bayes’ rule P ( B | A ) = P ( B ) P ( A | B ) P ( B ) P

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## This note was uploaded on 12/11/2010 for the course MATH MATH 2030 taught by Professor Sikh during the Winter '09 term at York University.

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mt2solns - York University MATH 2030 3.0AF (Elementary...

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