Question

Let’s assume that there are two dice, and we will roll one of them, but we don’t know which one. The probability of rolling either dice is 1/2. One of them is fair in the sense that all 6 outcomes are equally likely. The other die gives probability 1/3 to numbers 1 through 3 and zero probability to numbers 4-6.

a-)The first roll was a 4. What is the probability that it was the fair die?

b-)The first roll was a 3. What is the probability that it was the fair die?

Hint(Bayes Rule)

Answer #1

We roll two fair 6-sided dice, A and B. Each one of the 36
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c. Given that the two dice land on different numbers, ﬁnd the
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Consider rolling two fair six-sided dice.
a) Given that the roll resulted in sum of 8, find the
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conditional probability that doubles are rolled.
c) Given that the two dice land on different numbers, find the
conditional probability that at least one die is a 6.

Let’s say that you have three dice that are different colors;
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as you can:
b) rolling a 3 or 4 on the pink die AND a 3 or 4 on the grey die
on the same roll

A bag contains 1000 identical looking six-sided dice. All are
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all other outcomes being equally likely. I put my hand in the bag
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Rolling Snake Eyes
We roll two six-sided dice d1 and d2. What is
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We roll two six-sided dice d1 and d2 and at
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We roll two six-sided dice d1 and d2 and at
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We roll three fair six-sided dice.
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(b) What is the probability that we roll a sum of at least
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(c) Now we roll three fair dice n times. How large need n be in
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(b) Suppose now that each of the 7 6-sided dice are weighted the
same such that the probability of
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Question I: You roll 2 fair dice, one red and one
green.
a) What is the probability that the red die does land on
4? does not land on 4?
b) What is the probability that either die lands on 4?
that neither die lands on 4?
c) What is the probability that the sum of the dice is
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QUESTION 5: A 4-sided die is used for some games. This die can
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