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#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....
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...
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...
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...
The probability that the sum is 5 when you roll two dice is 1/9; the probability...
The probability that the sum is 5 when you roll two dice is 1/9; the probability that the sum is 6 when you roll two dice is 5/36. Suppose you play a game where you win if the sum is 5 or 6. What is the probability that you win? A. 1/2 B. 1/4 C. 2/3 D. 6/45 E. 6/36 Suppose a sorority is selling 650 raffle tickets to raise money for a local charity. You are going to be...
Part 2: Weighted Dice Suppose that I have some weighted dice with the following ‘probability distribution’:...
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...
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...
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...
4.54 Probability that sum of dice is a multiple of 4. Suppose you roll a pair...
4.54 Probability that sum of dice is a multiple of 4. Suppose you roll a pair of dice and you record the sum of the dice. What is the probability that the sum is a multiple of 4?
probability a)You roll a dice with six sides. What is the probability of rolling a 3...
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...
(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?
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...
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?
(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?
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