Question 4: You roll a fair die once. Define the events A = “the result is one of the numbers 1, 3, and 4”, B = “the result is one of the numbers 3, 4, 5, and 6”. • Are the events A and B independent? Jusitfy your answer using the definition of independence. • Are the events A and B independent? Jusitfy your answer using the definition of conditional probability.
Homework Answers
P(A) = 3/6 = 1/2
P(B) = 4/6 = 2/3
P(A and B) = 2/6 = 1/3
P(A) * P(B) = 1/2 * 2/3 = 1/3
As P(A) * P(B) is equal to P(A and B), events A and B are independent.
Add Answer to:
Question 4: You roll a fair die once. Define the events A = “the
result is...
Question 5: You are given a fair red die and a fair blue die, and roll...
Question 5: You are given a fair red die and a fair blue die,
and roll both dice uniformly at random and independently of each
other. Define the events A = “the sum of the results is at least
9”, B = “at least one of the two rolls results in a 2”, C = “at
least one of the two rolls results in a 5”. • Determine Pr(A),
Pr(B), and Pr(C). • Determine Pr(B | C). • Are the...
Probability and Random Processes for Engineers You roll a fair die twice: all 36 outcomes are...
Probability and Random Processes for
Engineers
You roll a fair die twice: all 36 outcomes are equally likely. Let A be the event that the first roll is 1, 2, or 3. Let B be the event that the second roll is 6. Finally, let C be the event that the sum of the rolls is even. (a) Show that any two of A, B, and C are independent (b) Are A, B, and C independent? Derive your answer two...
You roll a 6-sided die. The die has one to six spots on each side, with...
You roll a 6-sided die. The die has one to six spots on each side, with each count (1, 2, 3, 4, 5, or 6) appearing once. The die is fair: each side has an equal chance that it will be up when the die lands. What is the probability that you will roll a value greater than or equal to 2? Express your answer in decimal form to 3 decimal places.
We roll two fair 6-sided dice. (1) What is the probability that at least one die...
We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem. Problem 4. (8 points) We deal from a well-shuffled 52-card deck. What is the probability that the 13th card is...
3. Roll a fair die 10 times. Call a number in 1, 2, 3, 4, 5,...
3. Roll a fair die 10 times. Call a number in 1, 2, 3, 4, 5, 6 a loner if it is rolled exactly once on the 10 rolls. (For example, if the rolls are 1 5 6 4 4 4 6 2 4 1, then 5 and 2 are the only loners) a. Compute the probability that at leas tone of numbers 1, 2, 3 is a loner.
F. Roll a red die and a black die simultaneously. Show work (26) What is the...
F. Roll a red die and a black die simultaneously. Show work (26) What is the probability that the sum of two numbers is 4? (a) 1/12 (b) 1/9 (c) 1/6 (d) 1/5 (27) What is the conditional probability that the number on the red die is 3 given that the number on the black die is 5? (a) 1/6 (b) 1/3 (c) 1/2 (d) 1 (28) What is the conditional probability that the sum of two numbers is 4...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a)...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a)...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...
Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that...
Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem.
1. I have a six sided die. My suspicion is that the die is not fair, rather it is weighted to rol...
1. I have a six sided die. My suspicion is that the die is not fair, rather it is weighted to rol twos more often then expected with a fair die. To investigate this I roll the die 100 times. In those 100 rolls, I observe 21 twos. (a) Carefully define a population parameter in words that oblem (b) Use the population parameter defined in (a) to formulate (as equations) the null and alter- is ofinterest in this pro uative...
Question 5: You are given a fair red die and a fair blue die,
and roll both dice uniformly at random and independently of each
other. Define the events A = “the sum of the results is at least
9”, B = “at least one of the two rolls results in a 2”, C = “at
least one of the two rolls results in a 5”. • Determine Pr(A),
Pr(B), and Pr(C). • Determine Pr(B | C). • Are the...
Probability and Random Processes for
Engineers
You roll a fair die twice: all 36 outcomes are equally likely. Let A be the event that the first roll is 1, 2, or 3. Let B be the event that the second roll is 6. Finally, let C be the event that the sum of the rolls is even. (a) Show that any two of A, B, and C are independent (b) Are A, B, and C independent? Derive your answer two...
We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem. Problem 4. (8 points) We deal from a well-shuffled 52-card deck. What is the probability that the 13th card is...
Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem.
1. I have a six sided die. My suspicion is that the die is not fair, rather it is weighted to rol twos more often then expected with a fair die. To investigate this I roll the die 100 times. In those 100 rolls, I observe 21 twos. (a) Carefully define a population parameter in words that oblem (b) Use the population parameter defined in (a) to formulate (as equations) the null and alter- is ofinterest in this pro uative...
Most questions answered within 3 hours.
-
vector a has componets Ax and Ay, and makes an angle theta with
the y-axis. Select...
asked 6 minutes ago -
What were the problems of the american frontier after 1763 and how
did the British address...
asked 48 minutes ago -
Why
isn’t pentanol (CH3 CH2 CH2 CH2 CH2 OH) very soluble in
water?
asked 1 hour ago -
In preparing its bank reconciliation for the month of April
2018, Haskins, Inc. has available the...
asked 2 hours ago -
Your job is to do the following: build a Monster class as your
base class, along...
asked 2 hours ago -
Phosgene (COCl2) reacts with ammonia
(NH3), as shown in this reaction. If 1.2 grams of
COCl2...
asked 2 hours ago -
Wefald Company sold bonds with a face value of $675,000 for
$625,000. The bonds have a...
asked 3 hours ago -
Research predefined java packages. Select 2 packages and
describe what they provide. Explain briefly what type...
asked 3 hours ago -
A fair 9-sided die is tossed. Find P(4
or at least 5). That is, find the...
asked 3 hours ago -
Part of an ANOVA table is shown below.
Source of
Variation
Sum of
Squares
Degrees
of...
asked 3 hours ago -
The activation energy for the decomposition of N2O4 is 57.2.
kJ/mol. If the rate constant for...
asked 3 hours ago -
The structure and function of a neuron
Ion channels, ion flow, and membrane potential changes...
asked 3 hours ago