Given 2 six sided dice and a coin List macrostates List microstates What is the most...
Given 2 six sided dice and a coin List macrostates List microstates What is the most likely microstate? What is the most likely macrostate?
Part A: Consider rolling two standard six-sided dice. How many possible ways (microstates) are there to make the sum of the two dice add to seven (macro state)? а. 6 b. 3 с. 1 d. 7 flip a coin. What are the chances that every Part B: Twenty people each simultaneously coin will come up heads? a. 9.5 x 10A-7 % b. 1.9 х 10^-4 % c. 9.5 x 10^-5 % d. 50 Part C: Twenty people each simultaneously flip...
Tim rolls two six-sided dice and flips a coin.All of the following are possible outcomes, EXCEPT:Heads, 3,41. Tails, 62, 8, Heads5, 2 , Tails
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll one six-sided dice. What is the chance that you roll a 4? (If you rolled two dice, rolling a 4 means the sum of the dice is 4) O 1 2 3 36 1 2 1 6 + + 1 4 36 1 6 2 2 1 36 + -10 2 . 4 36 + 4 6 2 2
2. Suppose you have a four-sided dice, a six-sided dice and a 12-sided dice, each dice is fair. You roll the three dice once and let Z be the number of 4's showing. Find E(Z) using the indicator method.
(c) Assume you have two boxes and you have to place a coin into each box. You toss a coin and place it into box 1 without changing its orientation. The side of the coin facing up can be either head (blue) or tail (red). Then you toss a second coin and place it into box 2 without changing its orientation. You are interested in how many coins end up "head up" or blue. There are 4 different microstates. •...
A. consider tossing three coins, one after the other. How many different arrangements are possible? (answer 8 for 2^n) but the following I'm unsure about B. We will call each of the arrangments above a microstate. Arrange the microstates into groups according to the number of heads. We will call these groupings a macrostate. For example: HHH (3 heads) HHT (2 heads) How many macrostates are possible for three coin tosses? C. How many microstates correspond to the macrostate of...
Compute the probabilities of the following events: -rolling a 6 on a six sided dice -drawing a single card it being a either a 2 or a diamond -flipping a coin 3 times and getting 0 heads -flipping a coin 3 times and getting at least 1 heads
If you roll two fair sided six sided dice one time, what are the chances that those of the dice will come up a five?
(A) If you roll 3 six-sided dice, what is the probability of getting an overall score of 8? (B) If you roll 3 six-sided dice 4 times, what is the probability of getting an overall score of 8 four times in a row? (C) If you roll 3 six-sided dice 2 times, what is the probability of getting an overall score of 8 on the first roll and an overall score of 3 on the second roll?