## Basic Probability and Random Variables

Study Probability including both Discrete and Continuous.

1. The lottery is an interesting topic in the study of Probability as it illustrates the Rule of Multiplication since the Probability of a successful pick gets much more infinitesimal as the quantity of possible numbers expand. The rules to the lotteries vary considerably by state, with the Powerball and in the Mega Millions as well. In 2016, a record-setting lottery jackpot was seen in the Powerball topping $1.59 Billion. This large jackpot resulted from several changes in its rules including the cost of each chance rising from one to two dollars and the increase in the possible numbers in the picks. As a result the odds of winning the grand prize have grown to hundreds of millions to one. Despite the buying fervor during the run up to the $1.5 Billion jackpot, it is rare for the percent of the numbers that are covered for any one drawing to exceed 75 or 80%. For the lottery, people have adopted many different strategies including playing birthday numbers (1 – 31), simulating their own drawing, playing favorite numbers, etc. The efficacy of some of these strategies have waned as the list of numbers included in the drawings have grown far above the days of the month to 69 as in Powerball.

Let’s put the odds of winning the lottery in context:

The odds of becoming a lightning victim in the U.S. in any one year is 1 in 700,000. The oddsof being struck in your lifetime is 1 in 3,000. Lightning can kill people (3,696 deaths were recorded in the U.S. between 1959 and 2003) or cause cardiac arrest. Jun 24, 2005

FLASH FACTS ABOUT LIGHTNING – NATIONAL GEOGRAPHIC

https://news.

2. You know Subjective Probability is different than most which is based on math and formulas and often people talk about going with their Gut. What this usually amounts to is that an expert opinion is based on his/her knowledge and experience, such as the talking heads we see on the business cable network CNBC every day. There are some stock market luminaries, because of their longevity and/or wealth such as Warren Buffet, who may be considered superior to others.

3. There is a website known as TRUECar designed to provide new car buyers with pricing and market data. The TV commercial displays the Normal or Bell-Shaped Curve to represent the distribution of the prices people have paid for different (specified) cars in their market areas.

Do you think the data are actually Normally Distributed?

Why or why not?