A dice is rolled till "3" or "4" occurred. 1. Find an expected number of times...
A dice is rolled till "3" or "4" occurred.
1. Find an expected number of times we have to roll the dice till "3" or "4" occurs.
2. What is the probability that "3" or "4" occurred on the 3rd roll?
1. (0.5 points) Here we have _________________________________ distribution with parameter(s) ______________
which is equal to ________________________.
2. (0.5 points) An expected number of times we have to roll the dice till "3" or "4" occurs means, that we have to find ___________. The formula of _________________ it equal to _______________. Thus an expected number of times we have to roll the dice till "3" or "4" occurs is equal to _________________.
3. (0.5 points) The probability that "3" or "4" occurred on the 3rd roll can be calculated _____________________________.
It is equal to ____________________.
Homework Answers
1. (0.5 points) Here we have Geometric distribution with parameter p=probability of getting "3" or "4"
which is equal to 2/6=1/3.
2. (0.5 points) An expected number of times we have to roll the dice till "3" or "4" occurs means, that we have to find E(X), where X=random variable denoting number of times we have to roll the dice till "3" or "4" occurs. The formula of E(X) it equal to
. Thus an expected number of times we have to roll the dice till "3" or "4" occurs is equal to 3.
3. (0.5 points) The probability that "3" or "4" occurred on the 3rd roll can be calculated
It is equal to 0.1481.
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A dice is rolled till "3" or "4" occurred.
1. Find an expected number of times...
3. If a pair of dice is rolled 4 times (i.e., each die is rolled 4...
3. If a pair of dice is rolled 4 times (i.e., each die is rolled 4 times) and the sum of the dice is always less than or equal to 6, should we feel confident that the dice are not fair? 4. Repeat problem 3 if the pairs of dice are rolled 6 times instead of 4 times.
1. An eight-sided dice is rolled 24 times a) What is the expected number of times...
1. An eight-sided dice is rolled 24 times a) What is the expected number of times the dice shows 8? b) What is the probability that the dice shows a 8 the ex- pected number O (c) Using a normal approximation for the binomial distribu tion estimate the probability of rolling 8 six or more times
1). Two dice are rolled, and the results are added. Assuming that this number is greater...
1). Two dice are rolled, and the results are added. Assuming that this number is greater than or equal to 8, what is the probability that one of the dice rolled a 6? 2). In the game “raven’s beak,” a player rolls 6 dice, and wins if at least three of the dice roll the same number. What is the probability of winning?
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability...
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
1. Suppose 7 dice are rolled. The dice are 6-sided and fair. a). Find the probability...
1. Suppose 7 dice are rolled. The dice are 6-sided and fair. a). Find the probability that more than 5 dice show 2 or less (you may leave your answer in unsimplified form). I found this answer to be 5/729= 0.006859 b). Suppose we roll 7 dice and count the number showing 2 or less. We repeat this experiment over and over, each time counting the number showing 2 or less. What should we expect to compute as an average...
(2) Three dice are rolled. If each lands on a different number, find the probability that one is 3. (2) Three dice are rolled. If each lands on a different number, find the probability that one...
(2) Three dice are rolled. If each lands on a different number, find the probability that one is 3.
(2) Three dice are rolled. If each lands on a different number, find the probability that one is 3.
Exercise 10.17. We flip a fair coin. If it is heads we roll 3 dice. If...
Exercise 10.17. We flip a fair coin. If it is heads we roll 3 dice. If it is tails we roll 5 dice. Let X denote the number of sixes among the rolled dice. (a) Find the probability mass function of X. (b) Find the expected value of X.
Rolling Dice 2. A pair of dice is rolled. Here is the sample space (all of...
Rolling Dice 2. A pair of dice is rolled. Here is the sample space (all of the possible outcomes) of rolling a pair of dice. First Die a) In how many different ways can we roll a 7 (as the sum of the two dice)? What is the probability of rolling a 7? 2 3 4 5 6 7 3 4 5 6 7 8 b) In how many ways can we roll a sum that is divisible by 3?...
In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A...
In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A player can choose to save anywhere from 0 - 5 of the dice between rolls 1 and 2 and between rolls 2 and 3, meaning that the player can set aside certain dice before rolling the remaining dice if they choose to do so. Suppose that a given player does not take advantage of saving die rolls and instead rolls all 5 dice each...
Find the conditional probability. Round to 3 decimal places. If two fair dice are rolled, find...
Find the conditional probability. Round to 3 decimal places. If two fair dice are rolled, find the conditional probability of a sum of 8 given that the roll is a "double".
1. An eight-sided dice is rolled 24 times a) What is the expected number of times the dice shows 8? b) What is the probability that the dice shows a 8 the ex- pected number O (c) Using a normal approximation for the binomial distribu tion estimate the probability of rolling 8 six or more times
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
(2) Three dice are rolled. If each lands on a different number, find the probability that one is 3.
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Exercise 10.17. We flip a fair coin. If it is heads we roll 3 dice. If it is tails we roll 5 dice. Let X denote the number of sixes among the rolled dice. (a) Find the probability mass function of X. (b) Find the expected value of X.
Rolling Dice 2. A pair of dice is rolled. Here is the sample space (all of the possible outcomes) of rolling a pair of dice. First Die a) In how many different ways can we roll a 7 (as the sum of the two dice)? What is the probability of rolling a 7? 2 3 4 5 6 7 3 4 5 6 7 8 b) In how many ways can we roll a sum that is divisible by 3?...
Find the conditional probability. Round to 3 decimal places. If two fair dice are rolled, find the conditional probability of a sum of 8 given that the roll is a "double".
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