What is the expected number of rolls of a 10-sided die until 5 different numbers are...

What is the expected number of rolls of a 10-sided die until 5 different numbers are achieved?

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orchestra answered 2 years ago

A fair 6-sided die is rolled repeatedly. (a) Find the expected number of rolls needed to...

A fair 6-sided die is rolled repeatedly. (a) Find the expected number of rolls needed to get a 1 followed right away by a 2. Hint: Start by conditioning on whether or not the first roll is a 1. (b) Find the expected number of rolls needed to get two consecutive 1’s. (c) Let an be the expected number of rolls needed to get the same value n times in a row (i.e., to obtain a streak of n consecutive...

Consider the experiment of rolling a six-sided fair die. Let X denote the number of rolls...

Consider the experiment of rolling a six-sided fair die. Let X denote the number of rolls it takes to obtain the first 5, Y denote the number of rolls until the first 2, and Z denote the number of rolls until the first 4. Numerical answers are needed only for parts (a) and (b). Expressions are sufficient for parts (c), (d), and (e). a) E[X|Y = 1 or Z = 1] b) E[X|Y = 1 and Z = 2] c)...

A die is continuously rolled until the total sum of all rolls exceeds 325. What is...

A die is continuously rolled until the total sum of all rolls exceeds 325. What is the probability that at least 95 rolls are necessary?

a fair 6-sided die is rolled three times. What is the probability that all three rolls...

a fair 6-sided die is rolled three times. What is the probability that all three rolls are 2? Round the answer to four decimal places

17#7 A die is continuously rolled until the total sum of all rolls exceeds 250. What...

17#7 A die is continuously rolled until the total sum of all rolls exceeds 250. What is the probability that at least 80 rolls are necessary?

Alice rolls a pair of fair six-sided dice until a sum of 6 appears for the...

Alice rolls a pair of fair six-sided dice until a sum of 6 appears for the first time. Independently, Bob rolls two fair six-sided dice until he rolls a sum 7 for the first time. Find the probability that the number of times Alice rolls her dice is equal to or within one of the number of times Bob rolls his dice.

Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting...

Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting sum less than or equal to 5 for the first time on the 4th roll? Show your work to receive credit.

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. (a) What is the probability of rolling a 7? (b) What is the probability of rolling an odd number and a number greater than 8? (c) What is the probability of rolling an even number or a number greater than 9? (d) Suppose you roll the die,...

1. In 90 rolls of a six-sided die, the outcome of 1 appears 16 times. State...

1. In 90 rolls of a six-sided die, the outcome of 1 appears 16 times. State whether the difference between what occurred and what you would have expected by chance is statistically significant. Is the difference between what occurred and what is expected by chance statistically significant? No Yes 2. What is statistical inference? Why is it important? A.Statistical inference is the process of determining if the difference between what is observed and what is expected is too great to...

Problem 28. A fair six-sided die is rolled repeatedly and the rolls are recorded. When two...

Problem 28. A fair six-sided die is rolled repeatedly and the rolls are recorded. When two consecutive rolls are identical, the process is ended. Let S denote the sum of all the rolls made. Is S more likely to be even, odd or just as likely even as odd?

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