1. Suppose 7 dice are rolled. The dice are 6-sided and fair. a). Find the probability...
1. Suppose 7 dice are rolled. The dice are 6-sided and fair.
a). Find the probability that more than 5 dice show 2 or less (you may leave your answer in unsimplified form).
I found this answer to be 5/729= 0.006859
b). Suppose we roll 7 dice and count the number showing 2 or less. We repeat this experiment over and over, each time counting the number showing 2 or less. What should we expect to compute as an average of all of these counts?
Homework Answers
![7 fair dice are rolled, let X denote the number of dice showing 2 or less. So lets first calculate the probability that a die shows 2 or less. If Y, denotes the outcome of the ith die,iTn PIY, S 2]1,2,..,7 X = Number of Yi less than or equal to 2 has a Binomial (7능 ) distribution. a) To calculate P[ X> 5] 15 5 Now, PLX > 51- 6 37 729 b) let X, denote the number of dice showing 2 or less at the ith tlal of the experiment (rolling7 dice), n - 1,2 Let Xn*1Xn L.e the average of the n trials. we know X Xare id random variables with probability distribution Binomial (73) Now, XE(X)-7x2-1 in probability, so, for large value of tn the value that we should expect fromXn i 2.333](http://img.homeworklib.com/questions/8c5b40a0-6124-11ea-ba52-c7b344d18a44.png?x-oss-process=image/resize,w_560)
Add Answer to:
1. Suppose 7 dice are rolled. The dice are 6-sided and
fair.
a). Find the probability...
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?
1.) Suppose you roll two fair six-sided dice. What is the probabilty that I rolled a...
1.) Suppose you roll two fair six-sided dice. What is the probabilty that I rolled a total of 5? 2.) Suppose you roll two fair six-sided die and I announce that the sun of the two die is 6 or less. What is the probabilty that you rolled a total of 5?
1. A blue fair 6-sided dice and a red fair 6-sided dice are rolled at the...
1. A blue fair 6-sided dice and a red fair 6-sided dice are rolled at the same time. a) What is the probability of the sum of the dice equals 7, given 1 2 3 4 5 6 at least one of the dice shows a 3? 1 (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) 2 (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) (3.1) (3.2) (3.3) (3.4) (3.5) (3.6) (4.1) (4.2) (4.3) (4.4) (4.5) (4.6) 5 (5.1) (5.2) (5.3) (5.4) (5.5) (5.6)...
Suppose that 16 fair, 6-sided dice are rolled together (but independently). (a) What is the probability...
Suppose that 16 fair, 6-sided dice are rolled together (but independently). (a) What is the probability that the average face value (that is, after the roll, add the face values of all the dice together and then divide by 16) is between 3 and 4? (d) Let Y denote the total face value of the 16 dice after the roll. What is the mean and standard deviation of Y? (e) Now instead of rolling 16 dice, you roll n dice....
Problem #3: 5 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that...
Problem #3: 5 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least one die lands on 3 given that all 5 dice land on different numbers. 6) [2 marks] True or False: If X is the maximum of the 5 numbers from one roll, and Y is the minimum of the 5 numbers from one roll, then X and Y are independent random variables.
both 7 and 8 7. Suppose two dice are rolled. Find the probabilities of the following...
both 7 and 8
7. Suppose two dice are rolled. Find the probabilities of the following events a) the maximum of the two numbers rolled is less than or equal to 2; b) the maximum of the two numbers rolled is less than or equal to 3; c) the maximum of the two numbers rolled is exactly equal to 3 d) Repeat b) and c) for r instead of 3, for each z from 1 to 6. e) Denote by...
2. Suppose you have a four-sided dice, a six-sided dice and a 12-sided dice, each dice...
2. Suppose you have a four-sided dice, a six-sided dice and a 12-sided dice, each dice is fair. You roll the three dice once and let Z be the number of 4's showing. Find E(Z) using the indicator method.
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than...
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than or equal to 4 is rolled once again. Let X be the number of dice that show a number less than or equal to 4 on the first roll, and let Y be the total number of dice that show a number greater than 4 at the end. (a) Find the joint PMF of X and Y . (Show your final answer in a...
If we roll a red 6-sided die and a green 6-sided die (both are fair dice...
If we roll a red 6-sided die and a green 6-sided die (both are fair dice with the numbers 1-6 equally likely to be rolled), what is the probability that we get (i) A 5 on the green die AND a 3 on the red die? (ii) A 5 on the green die OR a 3 on the red die? (iii) A 5 on the green die GIVEN we rolled a 3 on the red die?
If sixteen 8-sided fair dice are rolled at the same time, what is the probability that...
If sixteen 8-sided fair dice are rolled at the same time, what is the probability that each number will appear twice?
1. A blue fair 6-sided dice and a red fair 6-sided dice are rolled at the same time. a) What is the probability of the sum of the dice equals 7, given 1 2 3 4 5 6 at least one of the dice shows a 3? 1 (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) 2 (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) (3.1) (3.2) (3.3) (3.4) (3.5) (3.6) (4.1) (4.2) (4.3) (4.4) (4.5) (4.6) 5 (5.1) (5.2) (5.3) (5.4) (5.5) (5.6)...
Suppose that 16 fair, 6-sided dice are rolled together (but independently). (a) What is the probability that the average face value (that is, after the roll, add the face values of all the dice together and then divide by 16) is between 3 and 4? (d) Let Y denote the total face value of the 16 dice after the roll. What is the mean and standard deviation of Y? (e) Now instead of rolling 16 dice, you roll n dice....
Problem #3: 5 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least one die lands on 3 given that all 5 dice land on different numbers. 6) [2 marks] True or False: If X is the maximum of the 5 numbers from one roll, and Y is the minimum of the 5 numbers from one roll, then X and Y are independent random variables.
both 7 and 8
7. Suppose two dice are rolled. Find the probabilities of the following events a) the maximum of the two numbers rolled is less than or equal to 2; b) the maximum of the two numbers rolled is less than or equal to 3; c) the maximum of the two numbers rolled is exactly equal to 3 d) Repeat b) and c) for r instead of 3, for each z from 1 to 6. e) Denote by...
2. Suppose you have a four-sided dice, a six-sided dice and a 12-sided dice, each dice is fair. You roll the three dice once and let Z be the number of 4's showing. Find E(Z) using the indicator method.
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago