Let S(sub k) denote the event that the sum of three fair typical six-sided dice is k. Assume that one die is red, one is green and one is blue so that the three dice are distinguishable. Compute P(S(sub k), for all values of k.
In order to find the probabilities we first count the number of outcomes which give us sum
Let S(sub k) denote the event that the sum of three fair typical six-sided dice is...
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...
Three six-sided dice are rolled. Let X be the sum of the dice. Determine the range of X and compute P(X = 18) and P(X ≤ 4).
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 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
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...
Two fair 6-sided dice are tossed. Let X denote the number appearing on the first die and let y denote the number appearing on the second die. Show that X, Y are independent by showing that P(X = x, Y = y) = P(X = x) x P(Y = y) for all (x,y) pairs.
1. Toss two fair dice and let E1 denote the event that the sum is 10 and E2 the event that the first is 3. Show that the two events are not independent. Construct two independent events. Construct 4 events that are not independent but such that they are pairwise independent. 1. Toss two fair dice and let E1 denote the event that the sum is 10 and E2 the event that the first is 3. Show that the two...
ur the uennitionls dò hot match any of the terms. 2.3. Problem. Three fair, six-sided dice colored red, green and blue are rolled. Calculate each of the following probabilities:
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...
1. Three 6-sided dice are tossed. Let X denote the sum of the 3 values that occur. (a) How many ways can we have X = 3. (b) How many ways can we have X = 4. (c) How many ways can we have X = 5. (d) How many ways can all three dice give the same value? (e) How many ways can the dice give three distinct values? (f) How many ways can the first toss be the...