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In an experiment, a die is rolled continually until a 6 appears, at which point the...
3. (10 points) A fair, 6-sided die is rolled continually until two consecutive 6s appear. Find...
3. (10 points) A fair, 6-sided die is rolled continually until two consecutive 6s appear. Find the expected number of rolls. (Hint: Ross Chapter 3, Exercise Q23)
5. A pair of dice is rolled until a sum of either 5 or 7 appears....
5. A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. (Hint: Let Fn denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n 1 rolls. Compute P(F) and argue that PF) is the desired probability.)
5. A pair of dice is rolled until a sum of either 5 or 7 appears....
5. A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. (Hint: Let Fn denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n 1 rolls. Compute P(Fn) and argue that Σ 1 P(F, ) is the desired probability.)
Problem 2. a. You flip a coin and roll a die. Describe the sample space of...
Problem 2. a. You flip a coin and roll a die. Describe the sample space of this experi ment b. Each of the 10 people flips a coin and rolls a die. Describe the sample space of this c. In the erperiment of part b. how many outcomes are in the event where nobody rolled d. Find the probability of the events in part c. What assumptions have you made? experiment. How many elements are in the sample space? a...
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...
Two strange dice (Die A and Die B) are rolled and their numbers showing are to...
Two strange dice (Die A and Die B) are rolled and their numbers showing are to be added together. Die A and one side that is a 1, while the other sides are 3’s. Die B has four sides that are 2’s and two sides that are 6’s. Complete this table showing the sample space for this event. + 1 3 3 3 3 3 2 2 2 2 6 6 P(sum of 5) = Using the same strange dice...
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 fair die is rolled in a board game to determine how many spaces a player...
A fair die is rolled in a board game to determine how many spaces a player can move on their turn. It has one of the numbers 1,2,3,4,5, or 6 on each of its faces.Let event A be rolling an even number and event B be rolling an odd number.Identify the numbers of each of the following:Provide your answer below:There are _______ outcomes in the sample space.There are _______ outcomes in event A.P(A)=_______ is the probability that you choose an...
#4. A 6 sided die is thrown repeatedly, until the first time (if ever) that a...
#4. A 6 sided die is thrown repeatedly, until the first time (if ever) that a is tossed. a. What is the sample space for this experiment? (Refer to a non-''generically as an f"- failure.) calculate P(A) what would be the most efficient way to calculate this? toss or later? b. Let A be the event that the first occurs at the 3"d throw or later. If you wanted to c(ptmall) iencralivs a fomula fox t probability of the si...
Multi-part question: Please show explanation and step by step work!! 1. An experiment involves flipping a...
Multi-part question:
Please show explanation and step by step work!!
1. An experiment involves flipping a coin and rolling a fair six-sided die once. Let event A a head and an odd number occuring) a. List all the sample points in the sample space for this experiment b. What is the probability associated to each sample point in the sample space? c. What sample points are contained in event A? d. What is the probability of event A?
3. (10 points) A fair, 6-sided die is rolled continually until two consecutive 6s appear. Find the expected number of rolls. (Hint: Ross Chapter 3, Exercise Q23)
5. A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. (Hint: Let Fn denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n 1 rolls. Compute P(F) and argue that PF) is the desired probability.)
5. A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. (Hint: Let Fn denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n 1 rolls. Compute P(Fn) and argue that Σ 1 P(F, ) is the desired probability.)
Problem 2. a. You flip a coin and roll a die. Describe the sample space of this experi ment b. Each of the 10 people flips a coin and rolls a die. Describe the sample space of this c. In the erperiment of part b. how many outcomes are in the event where nobody rolled d. Find the probability of the events in part c. What assumptions have you made? experiment. How many elements are in the sample space? a...
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...
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?
#4. A 6 sided die is thrown repeatedly, until the first time (if ever) that a is tossed. a. What is the sample space for this experiment? (Refer to a non-''generically as an f"- failure.) calculate P(A) what would be the most efficient way to calculate this? toss or later? b. Let A be the event that the first occurs at the 3"d throw or later. If you wanted to c(ptmall) iencralivs a fomula fox t probability of the si...
Multi-part question:
Please show explanation and step by step work!!
1. An experiment involves flipping a coin and rolling a fair six-sided die once. Let event A a head and an odd number occuring) a. List all the sample points in the sample space for this experiment b. What is the probability associated to each sample point in the sample space? c. What sample points are contained in event A? d. What is the probability of event A?
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