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 a green die and a red die. Let A be the event that the sum of the numbers shown is 7 and let B be the event that both dice show odd numbers. Are events A and B independent? Show your work. Thank you :)
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...
A 6-sided die rolled twice. Let E be the event "the first roll is a 5" and F F the event "the second roll is a 5". (a) Are the events E E and F F independent? Input Yes or No: (b) Find the probability of showing a 5 on both rolls. Write your answer as a reduced fraction. Answer:
Determine whether the events A and B are independent. A balanced die is rolled twice. Event A: The sum of the two rolls is 6 Event B: The first roll comes up 2 A. False B. True
A 6-sided die rolled twice. Let E E be the event "the first roll is a 2" and F F the event "the second roll is a 2". (a) Are the events E and F independent? Yes or No: (b) Find the probability of showing a 2 on both rolls. Write your answer as a reduced fraction.
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
Practice Problems 2 Due: Tuesday February 5 : Suppose you roll a weighted die so that the probabilities of each face showing is as follows Number Showing0.15 Probability 0.10 0.15 0.10 0.15 a. Solve for x b. What is the probability of rolling an even number? c. What is the probability of rolling two even numbers? Suppose you roll the dice two times. What is the probability that the sum of the two rolls is not equal to 8? d....
Suppose you roll a 12 sided die. Let E be the event that the roll is even and W be the event that the roll is greater than or equal to 7. If you were to roll the die and someone tells you that the result was even, what is the probability that the roll is greater than or equal to 7?
1. Roll the die 40 times and record the rolled values in the table below. These represent 40 observations of X. 2. Calculate the sample mean of your 40 rolls using Excel. This number represents a single observation of the random variable X (which, again, is a random variable representing the sample mean of 40 rolls of a die). Record the value for the sample mean in the space below: Sample Mean Observation (= first observation of X): 4. Do...