Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 2
September 14, 2010
1. Problem 1.15, page 5657 in the text.
A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know
that the first toss is a head than if we know that at least one of the tosses is a head. Is she right?
Does it make a difference if the coin is fair or unfair? How can we generalize Alice’s reasoning?
2. Problem 1.14, page 56 in the text.
We roll two fair 6sided dice.
Each one of the 36 possible outcomes is assumed to be equally
likely.
(a) Find the probability that doubles are rolled.
(b) Given that the roll results in a sum of 4 or less, find the conditional probability that doubles
are rolled.
(c) Find the probability that at least one die roll is a 6.
(d) Given that the two dice land on different numbers, find the conditional probability that at
least one die roll is a 6.
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 Spring '11
 Proasin
 Computer Science, Electrical Engineering, Conditional Probability, Probability, Alice, Dice, monty hall problem

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