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COULD YOUR ODDS BE WRONG? I have a simple question. You list the odds of matching only the powerball as one in 84 on the powerball "ways to win" page. From my understanding of statistics (I could be wrong, but I got an A), the odds of selecting one number out of a group is simply one over the number of choices. Since there are not 84 choices for the powerball, may I assume the balls are somehow "fixed" so that some are more common than others? Otherwise, the listed odds are somehow defying the laws of statistics. I am really very eager to hear your explanation, so please return my message. Thank you. Susan G., via Internet. This is one of most common questions we get about the statistics of the game. If you could play only the red Powerball, then your odds of matching it would indeed be 1 in 45. But to win the $1 prize for matching the red Powerball alone, you must do just that; match the red Powerball ALONE. When you bet a dollar and play the game, you might match one white ball and the red Powerball. You might match three white balls and the red Powerball. To determine the probability of matching the red Powerball alone, you have to factor in the chances of matching one or more of the white balls too. C.S. To win this last prize you must choose your six numbers so that only the Powerball number is correct. In the older version of the Powerball lottery this would be done as follows: there are 45 × C(45,5) = 54,979,155 ways to choose your six numbers. But here your first 5 numbers must come from the 40 numbers not drawn by the lottery. This can happen in C(40,5) = 658,008 ways. Now there is only one way to match the Powerball number, so overall you have 658,008 chances out of 54,979,155 to win this prize. This reduces to 1 chance in 83.55, or about 1 chance in 4, in agreement with the official lottery pronouncement. The same kind of reasoning of course carries over to the present version of the game. To find the chance of winning any one of the prizes we need only count the number of ways to win the prize and divide this by the total number of possible picks b. Let n(i) be the number of ways to win the ith prize. Then the values of n(i) are shown in Table 3 below. 5PDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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