Determine the Best Odds of Winning a Lottery A lottery player lives near the bor
ID: 3629847 • Letter: D
Question
Determine the Best Odds of Winning a Lottery
A lottery player lives near the border of two states. In State D, the lottery game is to pick 10 different numbers from the integers 1 through 51. In State P, the game is to pick 9 different numbers from the integers 1 through 61. In both states the winner is determined by lottery headquarters by having headquarters doing the specified draw, and awarding the prize to those players (if any) who match the selections picked. The lottery money if not won by anyone, goes all to charity, so there is no carry over to the next lottery.
The player wants to figure out which state has the best chances of winning. In other words, if the player buys one ticket from each state, in which state are they more likely to win?
(a) What are the chances of winning in D? Enter an exact integer, without a decimal point. Your answer must agree exactly with Maple TA's result in order to be graded as correct.
The odds of a lottery ticket winning in State D are one in .
(b) Calculate the chances of winning in P and compare it to your answer in (a). In which state has the better chances of winning? Enter a single letter, either D or P. (If you calculate that there is no difference in the odds, then enter P.)
Your answer: State ????? gives better odds.
Explanation / Answer
State D: Chances = 1/ (51 * 50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42) Explanation: You get one ticket out of all the possible tickets. You have 51 different possibilities for the first number, 50 for the second number, etc.... State P: Chances = 1 / (61 * 60 * 59 * 58 * 57 * 56 * 55 * 54 * 53) Explanation: You get one ticket out of all the possible tickets. You have 61 different possibilities for the first number, 60 for the second number, etc.... Therefore, Chances of winning in State D: 1/(4.6367760833856E16) = 2.156670889E-17 Chances of winning in State P: 1/(6.292979141E15) = 1.589072485E-16 (a) Chances of winning D: 1/(4.6367760833856E16) = 2.156670889E-17 (b) State P gives better odds.
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