a)
Explain the details of the lottery game you are presenting- what type, scratching or drawing, how many numbers
?
The lottery game I am presenting is drawing-based. This means that players will select numbers, and then those numbers will be randomly drawn from a pool of numbers to determine the winners. Players will have the option to choose between different sets of numbers, with each set containing varying numbers of numbers to choose from. For example, one set may have players choose five numbers out of 50 numbers, while another may have players choose six numbers out of a pool of 60 numbers. Once players have selected their numbers, they will submit their tickets and wait for the drawing.
The drawing will use a random number generator to ensure fairness and impartiality. After the drawing, the winning numbers will be announced, and players with tickets that match the winning numbers will be declared the winners. The prizes will vary depending on the specific
numbers chosen and the number of players with matching tickets. Players can also choose to play multiple sets of numbers, increasing their chances of winning. However, this will require purchasing numerous tickets. This lottery game offers players an exciting and fair chance to win big prizes by testing their luck
and selecting the correct numbers.
b) Can you calculate the probability of winning the jackpot and various consolation prizes in that game? Explain the math and outcomes
.
Yes, it is possible to calculate the probability of winning the jackpot and consolation prizes in a lottery game. To determine the probability of winning the jackpot, we must first calculate the possible combinations for the chosen set of numbers. For example, if players choose six numbers out of a pool of 60, the unlimited possible combinations would be 60 choose 6, which equals 50,063,860.
Next, we need to determine the number of winning combinations. For simplicity, let's assume there is only one winning combination for the jackpot. This means the probability of winning the
jackpot would be 1 out of 50,063,860, approximately 0.000002%. As for the consolation prizes, we would need to calculate the number of winning combinations for each prize level and then divide it by the total number of possible combinations. For example,
if there are three consolation prizes, with five matching numbers, four matching numbers, and three matching numbers, the probabilities would be: - 5 matching numbers: 60 choose 5 = 5,461,512 combinations = 1 in 5,461,512 probability = approximately 0.000018%
