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.
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Yes the event A and event B are independent because in event B both dies shows odd therefore there sum is always even which Nevers comes seven therefore therefore there intersection of both event are empty so they are independent.
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?
Two standard dice are rolled, one red, one green. Let A be the event that the red die is a either a 4 or a 6, let B be the event that the sum of the dice is grenter than 5 a. Find P(A) c. Find P(A | B) e. Find P(An B) . Find P(A'I B) 10. b. Find P(B) d. Find P(B | A) f. Find P(AnB') h Find P(A'UB) Are events A and B dependent or independent?...
7. Pairwise Independence. Roll a red 4-sided die and a white 4-sided die. A: the red die is even B: the white die is even C: the sum of the two dice is even a) Show that A, B, and C are pairwise independent. b) Show that A n B and C are NOT independent. 8. Roll a red 6-sided die and a white 6-sided die. D: red die is 1 or 2 or 3 Show that P(D กั E...
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...
Suppose you roll two dice. Assume one is red and one is blue so that they are distinguishable. Let A be the event "The sum of the two dice is 7." and B be the event "The red die is 4." and C be the event "The difference of the two dice is even." a.) Are A and B independent? Justify your answer. b.) Are B and C independent? Justify your answer. c.) Are A and C independent? Justify your...
1. Roll a pair of dice, one red and one green. Now, define the following events: A is the event that at least one of the dice will be an even number B is the event that the sum of the die will be equal to 7; C is the event that at least one of the dice is equal to 1 (a) Draw a picture of the sample space. (b) List all the outcomes for each of the events...
Please answer the questions clearly 1. Roll a pair of dice, one red and one green. Now, define the following events: A is the event that at least one of the dice will be an even number B is the event that the sum of the die will be equal to 7; C is the event that at least one of the dice is equal to 1 (a) Draw a picture of the sample space. (b) List all the outcomes...
3. Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die gets a 3, B be the event that the green die gets a 4, and C be the event that the total number showing on the two dice is 7. A. Are A and B independent? Explain. B. Are B and C independent? Explain.
You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(5 on green die and 3 on red die). (Enter your answer as a fraction.) 2 (c) Find P(3 on green die and 5 on red die). (Enter your answer as a fraction.) 3 (d) Find P((5 on green die and 3 on red die) or (3 on green die and 5 on red die)). (Enter your answer...
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.