 # Essay On Winning The Lottery

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Winning the Lottery Introduction: The lottery was first invented as a way for the government to generate revenue. Over time, the purpose of the lottery evolved into a form of gambling that involves the drawing of numbers to win a prize. In recent years, people around the world take the chance to participate in the lottery in hopes of becoming a millionaire. I have been around friends and family, who have heard the news that people around the world or themselves have won a prize from the lottery and how it is only a game of chance to have matching numbers with the winning ticket. Therefore, the idea of winning the lottery fascinated me and initiated my curiosity to ask the question what is the chance of winning the lottery out of the many…show more content…
For a score of x, C(6, x), describes the odds of selecting x winning numbers out of six of the possible winning numbers. Therefore, there are 6-x losing numbers. Because there are six winning numbers, there are 49-6=43 numbers to choose from the losing numbers. Therefore, the number of ways for choosing from the losing numbers is C(43,6-x). Thus, to calculate the probability of winning the lottery with x matching numbers out of the six possible winning numbers, I multiplied the number of ways to choose x winning numbers out of 6 with the number of ways to choose the remaining losing numbers and divided by the the total number of possibilities to win with all six matching numbers. Probability of winning with x matching numbers =C(k, x) * C(n-k, k-x)C(n,k) n = total number of objects k = total number of winning numbers x = total number of numbers matching the winning numbers This generalization is also known as the hypergeometric distribution, which is used to calculate probabilities when sampling without replacement. I will find the probabilities of having 0, 1, 2, 3, 4, 5, and 6 matches with the winning numbers by plugging the number of matches into the formula as x. P(x) =C(6, x) * C(43, 6-x)C(49, 6) x matches Calculation