Question

In: Statistics and Probability

Suppose you roll a fair 15 sided die. The numbers 1-15 appear once on different sides....

Suppose you roll a fair 15 sided die. The numbers 1-15 appear once on different sides. (Imagine a regular die with 12 sides instead of 6.) Answers may be left in formula form.

  1. (a) What is the probability of rolling a 7?

  2. (b) What is the probability of rolling an odd number and a number greater than 8?

  3. (c) What is the probability of rolling an even number or a number greater than 9?

  4. (d) Suppose you roll the die, record the number you see, and then roll it again. What is the probability that the sum of the die is 11?

  5. (e) Suppose you roll the die, record the number you see, and then roll it again. What is the probability of rolling a 3 and then rolling a 3 again?

Solutions

Expert Solution


Related Solutions

Suppose we roll a fair 6 sided die with the numbers [1,6] written on them. After...
Suppose we roll a fair 6 sided die with the numbers [1,6] written on them. After the first die roll we roll the die ? times where ? is the number on the first die roll. The number of points you score is the sum of the face-values on all die rolls (including the first). What is the expected number of points you will score?
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...
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. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...
You roll a fair six-sided die and don't look at it. What is the probability that...
You roll a fair six-sided die and don't look at it. What is the probability that it is a 5 given that your friend looks and tells you that it is greater than 2? Leave your answer as a fraction.
17#13 Suppose we roll a fair six-sided die and sum the values obtained on each roll,...
17#13 Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping once our sum exceeds 289. Approximate the probability that at least 76 rolls are needed to get this sum.
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 9. Event B: The sum is not...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 9 Event B: The sum is not...
Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the...
Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the minimum of the value from each die. a. What is the probability mass function(pmf) of X? b. Find the mean E[X] and variance V (X). c. Write the cumulative distribution function (cdf) of X in a tabular form. d. Write F(x) the cdf of X as a step function and give a rough sketch for this function.
You have two fair six-sided dice. The sides of each die are numbered from 1 to...
You have two fair six-sided dice. The sides of each die are numbered from 1 to 6. Suppose you roll each die once. Let ? be ???(??? 1,??? 2), and let ? be ???(??? 1,??? 2). a) Find the joint PMF of ? and ?. b) Find ???(?). c) Find ?[?+?]
Let ? be the number that shows up when you roll a fair, six-sided die, and,...
Let ? be the number that shows up when you roll a fair, six-sided die, and, let ? = ?^2 − 5? + 6. a. Find both formats for the distribution of ?. (Hint: tep forms of probability distributions are CDF and pmf/pdf.) b. Find F(2.35)
1. Players A and B each roll a fair 6-sided die. The player with the higher...
1. Players A and B each roll a fair 6-sided die. The player with the higher score wins £1 from the other player. If both players have equal scores, the game is a draw and no one wins anything. i. Let X denote the winnings of player A from one round of this game. State the probability mass function of X. Calculate the expectation E(X) and variance Var(X). ii. What is the conditional probability that player A rolls a 2...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT