Questions 1-7: Hector will roll two fair, six-sided dice at the same time.
Let A = the event that at least one die lands with the number 3 facing up.
Let B = the event that the sum of the two dice is less than 5.
1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”?
2. Calculate the probability that at least one die lands with 3 facing up and the sum of the two dice is less than 5.
3. What is the correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5”?
4. Calculate the probability that at least one die lands with 3 facing up if the sum of the two dice is less than 5.
5. What is the correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up”?
6. Calculate the probability that the sum of the two dice is not less than 5 if at least one die lands with 3 facing up.
7. Are A and B independent? Explain your reasoning.
Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let A =...
5. What is the correct set notation for the event that "the sum of the two dice is not less than 5 if at least one die lands with 3 facing up"? 6. Calculate the probability that the sum of the two dice is not less than 5 if at least one die lands with 3 facing up. 7. Are A and B independent? Explain your reasoning. Use for Questions 1-7: Hector will roll two fair, six-sided dice at the...
You have two fair six-sided dice and you roll each die once. You count the sum of the numbers facing up on each die. Let event A be "the sum is not a prime number." What is P(A) 06/12 06/11 05/11 05/12
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?
You roll two six-sided fair dice. a. Let A be the event that either a 4 or 5 is rolled first followed by an even number. P(A) = Round your answer to four decimal places. b. Let B be the event that the sum of the two dice is at most 5. P(B) = Round your answer to four decimal places. c. Are A and B mutually exclusive events? d. Are A and B independent events?
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) 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 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.
Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die is a three, given that the sum is greater than 6 7 The probability is 12 (Type an integer or a simplified fraction)
Three six-sided fair dice are rolled. The six sides are numbered 1,2,3,4,5,6. Let A be the event that the first die shows an even number, let B be the event that the second die shows an even number, and let C be the event that the third die shows an even number. Express each of the following events in terms of the named events described above: 1) the event that all three dice show even numbers 2) the event that...
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?