Suppose a six-sided die is rolled and the probability of each number occurring is proportional to...
Suppose a six-sided die is rolled and the probability of each
number occurring is proportional to itself,
i.e. P(1) = 1k; P(2) = 2k : : :. Give the probabilities for each
number being rolled so that the axioms of
probability are satised.
I thought the answer was 1/6 for each number, is this wrong?
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Suppose a six-sided die is rolled and the probability of each
number occurring is proportional to...
Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled...
I know Pk~1/k^5/2 just need the
work
Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
Help please ! A six sided die is rolled. What is the probability that the number...
Help please !
A six sided die is rolled. What is the probability that the number on top is at least 2? O B. 1/6
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a...
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a total of 5? B) Suppose I roll two fair six-sided die and I announce that the sum of the two die is 6 or less. What is the probability that I rolled a total of 5?
Suppose a fair six-sided die is rolled and then a card from a standard 52-card deck...
Suppose a fair six-sided die is rolled and then a card from a standard 52-card deck is chosen in random. What is the probability of the die showing a six and the chosen card being a king?
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil-...
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
a) If a single six-sided die is rolled five times, what is the probability that a...
a) If a single six-sided die is rolled five times, what is the probability that a 6 is thrown exactly three times? b) A person receives an average of one e-mail message per half-hour interval. Assume that e-mails are received randomly in time, find the probabilities that in a particular hour 0,1,2,3,4,5 messages are received.
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
5. A fair six sided die is rolled 10 times. Let X be the number of...
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A...
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...
Suppose I asked you to roll a fair six-sided die 6 times. You have already rolled...
Suppose I asked you to roll a fair six-sided die 6 times. You have already rolled the die for 5 times and six has not appeared ones. Assuming die rolls are independent, what is the probability that you would get a six in the next roll? 1/6 1/2 5/6 0 1
I know Pk~1/k^5/2 just need the
work
Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
Help please !
A six sided die is rolled. What is the probability that the number on top is at least 2? O B. 1/6
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
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