A state originally operated a 6/46 lottery, meaning that the grand prize went to

Question

A state originally operated a 6/46 lottery, meaning that the grand prize went to a player (or players) who picked the same six numbers that were later drawn at random from the set of numbers 1 through 46. In 1992, the state went to a 6/58 lottery, but later the state went to a 6/54 lottery. (a) Find the probability of winning a 6/46 lottery. (b) Find the probability of winning a 6/58 lottery. (c) Find the probability of winning a 6/54 lottery. (d) Why do you think the state changed to a 6/58 lottery? (e) Why do you think the state went to a 6/54 lottery?

Explanation / Answer

a) Number of possible combinations = 46C6 = 9366819

So,

P(Winning a 6/46 lottery) = 1/9366819

b) Number of possible combinations = 58C6 = 40475358

So,

P(Winning a 6/58 lottery) = 1/40475358

c) Number of possible combinations = 54C6 = 25827165

So,

P(Winning a 6/46 lottery) = 1/25827165

d) State changed it from 6/46 to 6/58 lottery so that more number of tickets can be generated and more people can buy that lottery.

e) It again changed from 6/58 to 6/54 because it might be the case that the number of lotteries were too high in case of 6/58 which demotivated the buyers.

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