Cash6 - 5 38 1 44 6 6 38 44 43 42 41 40 39 6 5 4 3 2 1 228...

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Calculating the probability of winning the Virginia Lotto The Virginia Lotto © requires you to pick 6 numbers (without replacement, i.e. no duplicates) between 1 and 44. To win a prize you must match either 3, 4, 5 or 6 of the randomly selected numbers. This is a hypergeometric distribution. The chance of getting exactly 3 numbers correct is: 6 3 38 3 44 6 6 5 4 3 2 1 38 37 36 3 2 1 44 43 42 41 40 39 6 5 4 3 2 1 20 8436 7059052 023901 F H G I K J F H G I K J F H G I K J = ⋅ ⋅ ⋅ ⋅ × ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = × = . Thus the chance of winning a free ticket is 1 in (.023901) -1 or 43.839. The chance of getting exactly 4 numbers correct is: 6 4 38 2 44 6 6 5 2 1 38 37 2 1 44 43 42 41 40 39 6 5 4 3 2 1 15 703 7059052 001493826 F H G I K J F H G I K J F H G I K J = × ⋅ ⋅ ⋅ ⋅ ⋅ = × = . Thus the chance of winning the $50 prize is 1 in (.001493826) -1 = 669.421 The chance of getting exactly 5 numbers correct is: 6
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Unformatted text preview: 5 38 1 44 6 6 38 44 43 42 41 40 39 6 5 4 3 2 1 228 7059052 00003229895 F H G I K J F H G I K J F H G I K J = = = . so the chance of winning $1000 is 1 in 30960.754. The chance of getting all 6 numbers correct is: 6 6 38 44 6 1 44 43 42 41 40 39 6 5 4 3 2 1 1 7059052 00000014166208 F H G I K J F H G I K J F H G I K J = = = . so the chance of winning the Jackpot is trivially one in 7059052. To put this in perspective, the odds that an automobile trip will end in death is about one in four million; therefore, if you jump in the car to drive to the Seven-Eleven to buy a lottery ticket, the chance of you dying in a traffic accident on the trip is approximately twice your chance of winning the jackpot....
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