# Probability : General Probability, Systems and Dice

Not what you're looking for?

2.17 Show that, if

(a) a fair die is thrown times independently, it is more likely than not that at least one six appears;

(b) a pair of fair dice are thrown 24 times independently, it is more likely than not that a double six does not appear.

(This pair of calculation has an honoured place in the history of the development of the formal study of probability. Some seventeenth century gamblers are said to have believed that, sin (a) holds, then having six times as many throws (4- 24) "ought" to give the same chance of getting an event that was one sixth as likely (six - double six). It is very satifying to see a loose argument give the wrong answer).

2.18 In the diagram, the numbers are the (independent) chances the components will fail within ten years. Find the chance the system fails with ten years.

Given that the system has not failed in ten years, find the chance neither component marked * has failed.

2.19 Poker die have six equally likely faces labeled { 9,10,J,Q,K,A}. When five such dice are thrown independently, what are the probabilities of the different types of "hand" which, in rank order are Five of a Kind(aaaaa); Four of a Kind(aaaab); Full House(aaabb); Three(aaabc); Two Pairs(aabbc); One Pair(aabcd); and no Pair(abcde)?

("Runs" are not normally considered in this game.)

Given any of these hands, you are allowed to roll again any dice that unmatched. Find your respective chances of improving your hand for the different initial holding (ignoring "improvements" such as turning (KKKQJ) to (KKKA9).

Partial solutions:

##### Purchase this Solution

##### Solution Summary

General Probability, Systems and Dice are investigated. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Probability Quiz

Some questions on probability

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.