<P> Many lotteries have a powerball (or "bonus ball"). If the powerball is drawn from a pool of numbers different from the main lottery, the odds are multiplied by the number of powerballs . For example, in the 6 from 49 lottery, given 10 powerball numbers, then the odds of getting a score of 3 and the powerball would be 1 in 56.66 × 10, or 566.6 (the probability would be divided by 10, to give an exact value of 8815 / 4994220). Another example of such a game is Mega Millions, albeit with different jackpot odds . </P> <P> Where more than 1 powerball is drawn from a separate pool of balls to the main lottery (for example, in the EuroMillions game), the odds of the different possible powerball matching scores are calculated using the method shown in the "other scores" section above (in other words, the powerballs are like a mini-lottery in their own right), and then multiplied by the odds of achieving the required main - lottery score . </P> <P> If the powerball is drawn from the same pool of numbers as the main lottery, then, for a given target score, the number of winning combinations includes the powerball . For games based on the Canadian lottery (such as the lottery of the United Kingdom), after the 6 main balls are drawn, an extra ball is drawn from the same pool of balls, and this becomes the powerball (or "bonus ball"). An extra prize is given for matching 5 balls and the bonus ball . As described in the "other scores" section above, the number of ways one can obtain a score of 5 from a single ticket is (6 5) (43 1) (\ displaystyle (6 \ choose 5) (43 \ choose 1)) or 258 . Since the number of remaining balls is 43, and the ticket has 1 unmatched number remaining, 1 / 43 of these 258 combinations will match the next ball drawn (the powerball), leaving 258 / 43 = 6 ways of achieving it . Therefore, the odds of getting a score of 5 and the powerball are 6 (49 6) (\ displaystyle (6) \ over (49 \ choose 6)) = 1 in 2,330,636 . </P> <P> Of the 258 combinations that match 5 of the main 6 balls, in 42 / 43 of them the remaining number will not match the powerball, giving odds of 258 ⋅ 42 43 (49 6) (\ displaystyle (258 \ cdot ((42) \ over (43))) \ over (49 \ choose 6)) = 3 / 166,474 (approximately 55,491.33) for obtaining a score of 5 without matching the powerball . </P>

How do you calculate the odds of winning the lottery