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Geometric Probability

     Geometric probability refers to a sub-topic in probability where geometric imagery is used, whether due to the nature of the question or the nature of the answer. A famous geometric probability is Buffon's needle. In this problem mathematician Compte de Buffon asks: if you have a needle of length L and drop it onto a floor lined with parallel cracks all distance D apart, what is the probability that, when dropped at random, the needle will be touching one of the cracks?

     Another example of a geometric probability question is: select three points at random on a circle. What is the distribution of the areas of triangles that are created by three points selected in this way? The list goes on, but as long as geometry is involved to solve such questions of probability, then it is considered a part of the sub-topic geometric probability.  

Business Statistics: Probability Sample Questions

See the attached file. Chapter 5  
1. Mutually exclusive events cannot be independent.  2. The probability of an event is always greater than zero and less than 1. 3. If events A and B are independent, then the probability of A given B, that is, P(A|B) is equal to 0. F 

4. Events that have no sample space

Determining Probability: Coin Toss Example Problem

Let N be the number of tosses with a fair coin until tails occurs. What is the characteristic function of N? What is the mean and variance of N? What is the pmf of N? What is the probability that N is an even number?

Geometric and Negative Binomials

The solution addresses the following: Suppose the random variable X has geometric distribution of P = 0.5, determine the following probabilities.... Consider a sequence of independent Bernolli trials with p = 0.2..... See attached file for full problem.

Probability - Geometric Distribution

In a recent year Barry Bonds hit 73 home runs in the 153 games he played. Assume that his home run production stayed at that level the following season. What is the probability that he would hit his first home run a) on the first game of the season b) on the second game of the season c) on the first or second game of the sea