#5. Suppose we roll three tetrahedral dice that have 1, 2, 3, and 4 on their...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
4. Suppose we roll N dice, where N is a random number, with P ( N = i ) = 2 − i for i ≥ 1 . The sum of the dice is denoted by S . Find the probability that: (a) (5 points) N = 2 given S = 4 ; (b) (5 points) N is even; (c) (5 points) S = 4 given N is even.
We roll 2 dice and sum the numbers on the faces. a) What is the probability that we roll a 5? b) What is the probability that we roll a 2 or a 3? c) What is the probability that we roll at least a 10? d) What is the probability that we roll at most a 5? e) What is the probability that we roll an even sum? f) What is the probability that we roll either an even...
Part 2: Weighted Dice Suppose that I have some weighted dice with the following ‘probability distribution’: Outcome 1 2 3 4 5 6 Probability 1/8 1/8 1/8 2/8 2/8 2/8 1) Is this a discrete or continuous probability distribution? What is wrong with it? 2) Here is a fixed version. Verify that it is a valid probability distribution. To do this, check that the first two probability rules apply. Outcome 1 2 3 4 5 6 Probability 1/9 1/9 1/9...
8. We roll two fair dice. (1) Given that the roll results in a sum of 6 or less, what is the conditional probability that doubles are rolled? A "double" means that two dice have the same number (2) Given that the two dice land on different numbers, what is the conditional proba- bility that at least one die roll is a 1?
A dice is rolled till "3" or "4" occurred. 1. Find an expected number of times we have to roll the dice till "3" or "4" occurs. 2. What is the probability that "3" or "4" occurred on the 3rd roll? 1. (0.5 points) Here we have _________________________________ distribution with parameter(s) ______________ which is equal to ________________________. 2. (0.5 points) An expected number of times we have to roll the dice till "3" or "4" occurs means, that we have to...
probability a)You roll a dice with six sides. What is the probability of rolling a 3 or a 4? b)You roll one dice, twice. What is the probability of rolling an even number the first time and a 1 the second time? c) There are ten marbles in a bag, three yellow, three blue and four red. You draw one marble out of the bag. What is the probability that the marble is yellow or blue?
(2) If we roll a pair dice, what is the probability that: (a) the sum is 8? (b) both are 3 providing that one of them is 3?
Exercise 10.17. We flip a fair coin. If it is heads we roll 3 dice. If it is tails we roll 5 dice. Let X denote the number of sixes among the rolled dice. (a) Find the probability mass function of X. (b) Find the expected value of X.
Suppose that you roll 112 fair six-sided dice. Find the probability that the sum of the dice is less than 400. (Round your answers to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question.