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CALCULATING THE PROBABILITIES OF WINNING LOTTO 6/49 VERSION 3 : MARCH 1, 2003 The probability of event tells us how likely it is that the event will occur and is always a value between 0 and 1 (e.g. “there is a 50% chance of rain tomorrow” means that the probability of rain is .50, or “that team has a 1 in 1000 shot at winning” means that the probability that the team will win is 1 = .001). A random event is very likely to happen if its probability is close to 1 and 1000 it is not likely to happen if the probability is close to 0. In the lottery, the probability of winning will be equal to the fraction of all of the possible lottery numbers which count as winning. That is, the probability of winning the lottery = the number of winning lottery numbers the total number of possible lottery numbers In order to find the probability of winning the lottery we will have to figure out “the number of winning lottery numbers” and “the total number of possible lottery numbers.” The number of ways of picking r items from a set of n items is denoted by n = n! where n! r r!(n−r)! represents n×(n−1)×(n−2)×···×2×1. The number of ways of picking 2 items from a set of 5 items is by this formula: 5 = 5·4·3·2·1 = 120 = 10. That is, if our set of 5 items is {1, 2, 3, 4, 5} then 2 3·2·1·2·1 12 we can pick the following 10 groups of 2 items: {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3, 4}, {3, 5}, {4, 5}. This is exactly what is needed to find the number of possible lottery numbers because in the lottery 6 numbers are chosen from a set of size 49. Since the number of ways of picking of 6 numbers from a set of 49 different numbers is 49 = 13,983,816, this is equal to the total number of possible 6 6/49 tickets. In order to win the large jackpot in the lottery you must hold a winning ticket which matches all 6 of the winning numbers and there is exactly one set of winning lottery numbers. Therefore, the probability of winning the large jackpot in the 6/49 lottery = 1 13, 983, 816 To figure out the probability of winning the other prizes in the lottery the method is always the same, determine the number of possible winning numbers and then divide by the total number of possible lottery numbers. 1PDF Image | CALCULATING THE PROBABILITIES OF WINNING LOTTO
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