(5) A fair 6-sided dice is rolled twice. The fairness of the dice consists of the...

(5) A fair 6-sided dice is rolled twice. The fairness of the dice consists of the following facts: (i) no face of the dice is likelier to be rolled than any other (so a roll of a 5 and a roll of a 3 are equiprobable) and (ii) the dice has no “memory” - each roll is independent of any other. 5.1:

What is the probability that you’ve first rolled a 3 and the pair of rolls sums to something more than 4?

5.2: Given that you’ve first rolled a 3, what is the probability of that the pair of rolls sums to something more than 4?

5.3: Given that the sum of the two rolls is either exactly 7 or exactly 6, what is the probability that the first roll is a 2 and the second roll is something greater than 3?

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orchestra answered 1 year ago

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