6. Assume you have a typical 6-sided die. That is to say, it has sides 1,...
1. Suppose Jane has a fair 4-sided die, and Dick has a fair 6-sided die. Each day,they roll their dice (independently) until someone rolls a “1”. (Then the personwho did not roll a “1” does the dishes.) Find the probability that …a) they roll the first “1” at the same time (after equal number of attempts);b) it takes Dick twice as many attempts as it does Jane to roll the first “1”;c) Dick rolls the first “1” before Jane does.
1) Suppose you have a six-sided die. The die, unlike normal ones, has three sides with number 1, one side with number 2, and two sides with number 3. You roll this die once. Define the rauou ariable X to b ihe wing up afer the roll. a) List all possible outcomes of the random variable X and the corresponding probabilities b) Calculate the mean and the variance of the random variable. X
You roll a 6-sided die. The die has one to six spots on each side, with each count (1, 2, 3, 4, 5, or 6) appearing once. The die is fair: each side has an equal chance that it will be up when the die lands. What is the probability that you will roll a value greater than or equal to 2? Express your answer in decimal form to 3 decimal places.
i. Consider a weighted 6-sided die that is twice as likely to produce any even outcome as any odd outcome. What is the expected value of 1 roll of this die? What is the expected value of the sum of 9 rolls of this die? ii. Let X denote the value of the sum of 10 rolls of an unweighted 6-sided die. What is Pr(X = 0 mod 6)? (Hint: it is sufficient to consider just the last roll) *side...
You have two fair, 6-sided dice. Die 1 has 4 white faces and 2 black faces. Die 2 has 2 white faces and 4 black faces. You roll Die 1. If it comes up white, then Die 1 is the “chosen die” and you put Die 2 away, but if it comes up black, then Die 2 is the “chosen die” and you put Die 1 away. You now roll the chosen die twice, noting the color that comes up...
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
Question 3 3 pts Matching problem [Choose] You roll a fair six-sided die 500 times and observe a 3 on 90 of the 500 rolls. You estimate the probability of rolling a 3 to be 0.18 Choose) You roll a fair six-sided die 10 times and observe a 3 on all 10 rolls. You bet the probability of rolling a 3 on the next rollis close to O since you have already had 10 3's in a row You assign...
suppose you only have one fair 6-sided die. We will say that a success is if you roll a 5 or a 6. You roll the die over and over until you roll two successes in a row. What is the the expected number of times you must roll before you stop?
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:
6. A fair six sided die is rolled three times. Find the probability that () all three rolls are either 5 or 6 (6) all three rolls are even (c) no rolls are 5 (d) at least one roll is 5 (e) the first roll is 3, the second roll is 5 and the third roll is even