Question 3 3 pts Matching problem [Choose] You roll a fair six-sided die 500 times and...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
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
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
You roll a fair six-sided die 5 times. What is the probability that EXACTLY one of the rolls lands on 1 (round your answer to 2 decimal places)? 10 4/8
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
Consider a fair six-sided die. (a) What is its probability mass function? Graph it. It represents the population distribution of outcomes of rolls of a six-sided die (b) How would you describe the population distribution? (c) What is the sampling distribution of x for a six-sided fair die, when its rolled 100 times? Describe it with as much specificity as possible. NOTE: Roll of a die is a discrete variable. Why is it ok to use the Normal distribution to...
1. I have a six sided die. My suspicion is that the die is not fair, rather it is weighted to rol twos more often then expected with a fair die. To investigate this I roll the die 100 times. In those 100 rolls, I observe 21 twos. (a) Carefully define a population parameter in words that oblem (b) Use the population parameter defined in (a) to formulate (as equations) the null and alter- is ofinterest in this pro uative...
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...
You roll a fair 6-sided die 1000 times and determine your “score” by summing over all your rolls. What are the average, variance and standard deviation of your score for this game? What is the probability that you scored less than 3300? That you scored more than 3600?
we repeatedly roll a fair 8-sided die six times and suppse X is the number of different values rolled. Find E[x] and E[Y]